arXiv subjects

Sayan Banerjee

Publications and source records attributed to Sayan Banerjee.

At least 37 records · Page 2Linked to original sources

arXiv2025

Correlations between superconducting and resistive anisotropies

There are multiple possible origins of transport anisotropies in metals and superconductors. For instance, rotational symmetry can be spontaneously broken in the normal state as a result of electronic nematic order inducing anisotropies in an otherwise $s$-wave superconducting phase. Another possibility is that the dominant source of rotational symmetry breaking is the superconductor itself and its vestiges that may survive in the normal state. We here theoretically analyze the correlations of transport anisotropies in the normal and the corresponding superconducting phase for different scenarios of broken symmetry, either coming solely from the normal state, solely from the superconductor and its vestiges in the metallic regimes, or from both simultaneously. We further include both zero-momentum and finite-momentum pairing; we develop a theory of vestigial order for the latter, characterized by broken rotational and translational symmetry. Our findings reveal that the relative transport anisotropies in the normal and superconducting phases sensitively depend on the scenario, including the form of vestigial order and, in some cases, the parity of the superconducting order parameter. As such, measuring the directional dependence of the critical current and resistivity can provide strong constraints on the origin of rotational symmetry breaking. We demonstrate our findings in minimal models relevant to twisted multilayer graphene, rhombohedral graphene, and twisted transition metal dichalcogenides.

cond-mat.supr-con↗

arXiv2025

Attribute network models, stochastic approximation, and network sampling and ranking algorithms

We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation techniques we show that, in the large network limit, such networks converge in the local weak sense to limiting infinite random trees with an explicit description in terms of randomly stopped multi-type branching processes. This allows for the derivation of asymptotics for a wide class of network functionals implying, for example, that while degree distribution tail exponents depend on the attribute type (already derived by Jordan (2013)), PageRank centrality scores have the same tail exponent across attributes. The limit results also give explicit formulae for the performance of various network sampling mechanisms. One surprising consequence is the efficacy of PageRank and walk based network sampling schemes for directed networks in the setting of rare minorities.

math.PR↗

arXiv2025

Network evolution with mesoscopic delay

Owing to the influence of real-world networks both in science and society, numerous mathematical models have been developed to understand the structure and evolution of these systems, particularly in a temporal context. Recent advancements in fields like distributed cyber-security and social networks have spurred the creation of probabilistic models of evolution, where individuals make decisions based on only partial information about the network's current state. This paper seeks to explore models incorporating network delay, where new participants receive information from a time-lagged snapshot of the system. In the context of mesoscopic network delays, we develop probabilistic tools built on stochastic approximation to understand asymptotics of both local functionals, such as local neighborhoods and degree distributions, as well as global properties, such as the evolution of the degree of the network's initial founder. A companion paper explores the regime of macroscopic delays in the evolution of the network.

math.PR↗

arXiv2025

On the Structure of Stationary Solutions to McKean-Vlasov Equations with Applications to Noisy Transformers

We study stationary solutions of McKean-Vlasov equations on the circle. Our main contributions stem from observing an exact equivalence between solutions of the stationary McKean-Vlasov equation and an infinite-dimensional quadratic system of equations over Fourier coefficients, which allows explicit characterization of the stationary states in a sequence space rather than a function space. This framework provides a transparent description of local bifurcations, characterizing their periodicity, and resonance structures, while accommodating singular potentials. We derive analytic expressions that characterize the emergence, form and shape (supercritical, critical, subcritical or transcritical) of bifurcations involving possibly multiple Fourier modes and connect them with discontinuous phase transitions. We also characterize, under suitable assumptions, the detailed structure of the stationary bifurcating solutions that are accurate upto an arbitrary number of Fourier modes. At the global level, we establish regularity and concavity properties of the free energy landscape, proving existence, compactness, and coexistence of globally minimizing stationary measures, further identifying discontinuous phase transitions with points of non-differentiability of the minimum free energy map. As an application, we specialize the theory to the Noisy Mean-Field Transformer model, where we show how changing the inverse temperature parameter $β$ affects the geometry of the infinitely many bifurcations from the uniform measure. We also explain how increasing $β$ can lead to a rich class of approximate multi-mode stationary solutions which can be seen as `metastable states'. Further, a sharp transition from continuous to discontinuous (first-order) phase behavior is observed as $β$ increases.

math.PR↗

arXiv2025

Fluctuations of the Atlas model from inhomogeneous stationary profiles

The infinite Atlas model describes the evolution of a countable collection of Brownian particles on the real line, where the lowest particle is given a drift of $γ\in [0,\infty)$. We study equilibrium fluctuations for the Atlas model when the system of particles starts from an inhomogeneous stationary profile with exponentially growing density. We show that the appropriately centered and scaled occupation measure of the particle positions, with suitable translations, viewed as a space-time random field, converges to a limit given by a certain stochastic partial differential equation (SPDE). The initial condition for this equation is given by a Brownian motion, the equation is driven by an additive space-time noise that is white in time and colored in space, and the linear operator governing the evolution is the infinitesimal generator of a geometric Brownian motion. We use this SPDE to also characterize the fluctuations of the ranked particle positions with a suitable centering and scaling. Our results describe the behavior of the particles in the bulk and one finds that the Gaussian process describing the asymptotic fluctuations has the same Hölder regularity as a fractional Brownian motion with Hurst parameter $1/4$. One finds that, unlike the setting of a homogeneous profile (Dembo and Tsai (2017)), the behavior on the lower edge of the particle system is very different from the bulk behavior and in fact the variance of the Gaussian limit diverges to $\infty$ as one approaches the lower edge. Indeed, our results show that, with the gaps between particles given by one of the inhomogeneous stationary distributions, the lowest particle, started from $0$, with a linear in time translation, converges in distribution to an explicit non-Gaussian limit as $t\to \infty$.

math.PR↗

arXiv2025

Many-server asymptotics for Join-the-Shortest Queue in the Super-Halfin-Whitt Scaling Window

The Join-the-Shortest Queue (JSQ) policy is a classical benchmark for the performance of many-server queueing systems due to its strong optimality properties. While the exact analysis of the JSQ policy is an open question to date, even under Markovian assumption on the service requirements, recently, there has been a significant progress in understanding its many-server asymptotic behavior since the work of Eschenfeldt and Gamarnik (Math.~Oper.~Res.~43 (2018) 867--886). In this paper, we analyze the many-server limits of the JSQ policy in the \emph{super-Halfin-Whitt} scaling window when load per server $λ_N$ scales with the system size $N$ as $\lim_{N\rightarrow\infty}N^α(1-λ_N)=β$ for $α\in (1/2, 1)$ and $β>0$. We establish that the centered and scaled total queue length process converges to a certain Bessel process with negative drift and the associated centered and scaled steady-state total queue length, indexed by $N$, converges to a $\mathrm{Gamma}(2,β)$ distribution. Both the transient and steady-state limit laws are universal in the sense that they do not depend on the value of the scaling parameter $α$, and exhibit fundamentally different qualitative behavior from both the Halfin-Whitt regime ($α= 1/2$) and the Non-degenerate Slowdown (NDS) regime ($α=1$).

math.PR↗

arXiv2025

Precision Agriculture Revolution: Integrating Digital Twins and Advanced Crop Recommendation for Optimal Yield

With the help of a digital twin structure, Agriculture 4.0 technologies like weather APIs (Application programming interface), GPS (Global Positioning System) modules, and NPK (Nitrogen, Phosphorus and Potassium) soil sensors and machine learning recommendation models, we seek to revolutionize agricultural production through this concept. In addition to providing precise crop growth forecasts, the combination of real-time data on soil composition, meteorological dynamics, and geographic coordinates aims to support crop recommendation models and simulate predictive scenarios for improved water and pesticide management.

cs.LG↗

arXiv2025

Local weak limits for collapsed branching processes with random out-degrees

We obtain local weak limits in probability for Collapsed Branching Processes (CBP), which are directed random networks obtained by collapsing random-sized families of individuals in a general continuous-time branching process. The local weak limit of a given CBP, as the network grows, is shown to be a related continuous-time branching process stopped at an independent exponential time. The proof involves the construction of an explicit coupling of the in-components of vertices with the limiting object. We also show that the in-components of a finite collection of uniformly chosen vertices locally weakly converge (in probability) to i.i.d. copies of the above limit, reminiscent of propagation of chaos in interacting particle systems. We obtain as special cases novel descriptions of the local weak limits of directed preferential and uniform attachment models. We also outline some applications of our results for analyzing the limiting in-degree and PageRank distributions. In particular, upper and lower bounds on the tail of the in-degree distribution are obtained and a phase transition is detected in terms of the growth rate of the attachment function governing reproduction rates in the branching process.

math.PR↗

arXiv2025

Dissipation-enhanced non-reciprocal superconductivity: application to multi-valley superconductors

We here propose and study theoretically a non-equilibrium mechanism for the superconducting diode effect, which applies specifically to the case where time-reversal-symmetry -- a prerequisite for the diode effect -- is spontaneously broken by the superconducting electrons themselves. We employ a generalized time-dependent Ginzburg-Landau formalism to capture dissipation effects in the non-equilibrium current-carrying state via phase slips and show that the coupling of the resistive current to the symmetry-breaking order is enough to induce a diode effect. Depending on parameters, the critical current asymmetry can be sizeable, asymptotically reaching a perfect diode efficiency; the competition of symmetry-breaking order, superconducting and resistive currents gives rise to rich physics, such as current-stabilized, non-equilibrium superconducting correlations. Although our mechanism is more general, the findings are particularly relevant to twisted trilayer and rhombohedral tetralayer graphene, where the symmetry-breaking order parameter refers to the imbalance of the two valleys of the systems.

cond-mat.supr-con↗

arXiv2024

Altermagnetic superconducting diode effect

Non-reciprocal superconductivity, also known as the superconducting diode effect, has been extensively studied in the presence of a magnetic field or some form of ferromagnetic order breaking time-reversal symmetry. We here show that another class of magnetic order known as altermagnetism, which also breaks time-reversal symmetry but does not exhibit a finite net magnetic moment, can also give rise to a superconducting diode effect. Whether this is the case depends on the combination of the system's point group and altermagnetic order parameter which we explore systematically for two-dimensional crystalline systems. If the superconducting electrons are in a centrosymmetric crystalline environment, an electric field $E_z$ (or other sources of inversion symmetry breaking) can be used to turn on and tune the non-reciprocity, yielding an electric-field tunable diode effect; there are also non-centrosymmetric point groups, which are not reached by applying $E_z \neq 0$ in a centrosymmetric crystal, but still allow for an altermagnetic order parameter with non-reciprocal superconductivity. Depending on the residual magnetic point group, the zeros of the critical current asymmetry, $J_c(\hat{n}) - J_c(-\hat{n})$, are pinned along high-symmetry crystalline directions $\hat{n}=\hat{e}_j$ or are free to rotate in the plane of the system. In some cases, the zeros can be rotated by tuning the electric field $E_z$. We discuss all of these phenomena both on the general level using exact symmetry arguments and more explicitly by constructing and solving minimal lattice models. We provide experimental setups to realize the altermagnetic superconducting diode effect.

cond-mat.supr-con↗

arXiv2024

Extremal Invariant Distributions of Infinite Brownian Particle Systems with Rank Dependent Drifts

\noindent Consider an infinite collection of particles on the real line moving according to independent Brownian motions and such that the $i$-th particle from the left gets the drift $g_{i-1}$. The case where $g_0=1$ and $g_{i}=0$ for all $i \in \mathbb{N}$ corresponds to the well studied infinite Atlas model. Under conditions on the drift vector $\boldsymbol{g} = (g_0, g_1, \ldots)'$ it is known that the Markov process corresponding to the gap sequence of the associated ranked particles has a continuum of product form stationary distributions $\{π_a^{\boldsymbol{g}}, a \in S^{\boldsymbol{g}}\}$ where $S^{\boldsymbol{g}}$ is a semi-infinite interval of the real line. In this work we show that all of these stationary distributions are extremal and ergodic. We also prove that any product form stationary distribution of this Markov process that satisfies a mild integrability condition must be $π_a^{\boldsymbol{g}}$ for some $a \in S^{\boldsymbol{g}}$. These results are new even for the infinite Atlas model. The work makes progress on the open problem of characterizing all the invariant distributions of general competing Brownian particle systems interacting through their relative ranks. Proofs rely on synchronous and mirror coupling of Brownian particles and properties of the intersection local times of the various particles in the infinite system.

math.PR↗

arXiv2024

Local weak convergence and its applications

Motivated in part by understanding average case analysis of fundamental algorithms in computer science, and in part by the wide array of network data available over the last decade, a variety of random graph models, with corresponding processes on these objects, have been proposed over the last few years. The main goal of this paper is to give an overview of local weak convergence, which has emerged as a major technique for understanding large network asymptotics for a wide array of functionals and models. As opposed to a survey, the main goal is to try to explain some of the major concepts and their use to junior researchers in the field and indicate potential resources for further reading.

math.PR↗

arXiv2024

Co-evolving dynamic networks

We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the direction of the root, connecting to the terminal vertex. Specific choices of the exploration step distribution lead to the well-studied affine preferential attachment and uniform attachment models, as well as less well understood dynamic network models with global attachment functionals such as PageRank scores [Chebolu-Melsted (2008)]. We obtain local weak limits for such networks and use them to derive asymptotics for the limiting empirical degree and PageRank distribution. We also quantify asymptotics for the degree and PageRank of fixed vertices, including the root, and the height of the network. Two distinct regimes are seen to emerge, based on the expected exploration distance of incoming vertices, which we call the `fringe' and `non-fringe' regimes. These regimes are shown to exhibit different qualitative and quantitative properties. In particular, networks in the non-fringe regime undergo `condensation' where the root degree grows at the same rate as the network size. Networks in the fringe regime do not exhibit condensation. Non-trivial phase transition phenomena are displayed for the height and the PageRank distribution, the latter connecting to the well known power-law hypothesis. In the process, we develop a general set of techniques involving local limits, infinite-dimensional urn models, related multitype branching processes and corresponding Perron-Frobenius theory, branching random walks, and in particular relating tail exponents of various functionals to the scaling exponents of quasi-stationary distributions of associated random walks. These techniques are expected to shed light on a variety of other co-evolving network models.

math.PR↗

arXiv2024

Load Balancing in Parallel Queues and Rank-based Diffusions

Consider a system with $K$ parallel queues in which the server for each queue processes jobs at rate $n$ and the total arrival rate to the system is $nK-\upsilon \sqrt{n}$ where $\upsilon \in (0, \infty)$ and $n$ is large. We study rank-based routing policies in which $O(\sqrt{n})$ of the incoming jobs are routed to servers with probabilities depending on their ranked queue-length and the remaining jobs are routed uniformly at random. A particular case, referred to as the marginal join-the-shortest-queue (MJSQ) policy, is one in which the $O(\sqrt{n})$ jobs are routed using the join-the-shortest-queue (JSQ) policy. Our first result provides a heavy traffic approximation theorem for such queuing systems. It turns out that, unlike the JSQ system, there is no state space collapse in the setting of MJSQ (and for the more general rank-based routing schemes) and one obtains a novel diffusion limit which is the constrained analogue of the well studied Atlas model (and other rank-based diffusions) arising from mathematical finance. Next, we prove an interchange of limits result which shows that the steady state of the queuing system is well approximated by that of the limiting diffusion, given explicitly in terms of product laws of Exponential random variables. Using these results, we compute the time asymptotic total queue-length in the heavy traffic limit for the MJSQ system. We find the striking result that although in going from JSQ to MJSQ the communication cost is reduced by a factor of $\sqrt{n}$, the asymptotic total queue-length increases only by a constant factor which can be made arbitrarily close to one by increasing a MJSQ parameter. When the system is overloaded ($\upsilon<0$) we show that although the $K$-dimensional MJSQ system is unstable, the steady state difference between the maximum and minimum queue-lengths stays bounded in probability (in the heavy traffic parameter $n$).

math.PR↗

arXiv2023

Automated Discovery of Wurtzite Solid Solutions with Enhanced Piezoelectric Response

While many piezoelectric materials are known, there is still great potential to improve on the figures of merit of existing materials through compositional doping, forming solid solutions. Specifically, it has been shown that doping and alloying wurtzite-structured materials can improve the piezoelectric response; however, a vast compositional space has remained unexplored. In this work, we apply a multi-level screening protocol combining machine learning, chemical intuition, and thermodynamics to systematically discover dopant combinations in wurtzite material space that improve the desired piezoelectric response. Through our protocol, we use computationally inexpensive screening calculations to consider more than 3000 possible ternary wurtzite solid solutions from 9 different wurtzite base systems: AlN, BeO, CdS, CdSe, GaN, ZnO, ZnS, ZnSe, and AgI. Finally, based on thermodynamic analysis and explicit piezoelectric response calculations, we predict 11 materials with improved piezoelectric response, due to the incorporation of electropositive dopants.

cond-mat.mtrl-sci↗

arXiv2023

Enhanced Superconducting Diode Effect due to coexisting Phases

The superconducting diode effect refers to an asymmetry in the critical supercurrent $J_c(\hat{n})$ along opposite directions, $J_c(\hat{n})\neq J_c(-\hat{n})$. While the basic symmetry requirements for this effect are known, it is, for junction-free systems, difficult to capture within current theoretical models the large current asymmetries $J_c(\hat{n})/J_c(-\hat{n})$ recently observed in experiment. We here propose and develop a theory for an enhancement mechanism of the diode effect arising from spontaneous symmetry breaking. We show - both within a phenomenological and a microscopic theory - that there is a coupling of the supercurrent and the underlying symmetry-breaking order parameter. This coupling can enhance the current asymmetry significantly. Our work might not only provide a possible explanation for recent experiments on trilayer graphene but also pave the way for future realizations of the superconducting diode effect with large current asymmetries.

cond-mat.supr-con↗

arXiv2023

PageRank Nibble on the sparse directed stochastic block model

We present new results on community recovery based on the PageRank Nibble algorithm on a sparse directed stochastic block model (dSBM). Our results are based on a characterization of the local weak limit of the dSBM and the limiting PageRank distribution. This characterization allows us to estimate the probability of misclassification for any given connection kernel and any given number of seeds (vertices whose community label is known). The fact that PageRank is a local algorithm that can be efficiently computed in both a distributed and asynchronous fashion, makes it an appealing method for identifying members of a given community in very large networks where the identity of some vertices is known.

math.PR↗

arXiv2023

Degree centrality and root finding in growing random networks

We consider growing random networks $\{\mathcal G_n\}_{n \ge 1}$ where, at each time, a new vertex attaches itself to a collection of existing vertices via a fixed number $m \ge 1$ of edges, with probability proportional to an attachment function $f$ of their degree. It was shown in \cite{BBpersistence} that such network models exhibit two regimes: (i) the persistent regime, corresponding to $\sum_{i=1}^{\infty}f(i)^{-2} < \infty$, where the top $K$ maximal degree vertices fixate over time for any given $K$, and (ii) the non-persistent regime, with $\sum_{i=1}^{\infty}f(i)^{-2} = \infty$, where the identities of these vertices keep changing infinitely often over time. We develop root finding algorithms using the empirical degree structure and local network information based on a snapshot of such a network at some large time. In the persistent regime, the algorithm is purely based on degree centrality, that is, for a given error tolerance $\varepsilon \in (0,1)$, there exists $K_{\varepsilon}$ such that for any $n \ge 1$, the confidence set for the root in $\mathcal G_n$, which contains the root with probability at least $1 - \varepsilon$, consists of the top $K_{\varepsilon}$ maximal degree vertices. In particular, the size of the confidence set is stable in the network size. Upper and lower bounds on $K_{\varepsilon}$ are explicitly characterized in terms of the error tolerance $\varepsilon$ and the attachment function $f$. In the non-persistent regime, for an appropriate choice of $r_n \rightarrow \infty$ at a rate much smaller than the diameter of the network, the neighborhood of radius $r_n$ around the maximal degree vertex is shown to contain the root with high probability, and a size estimate for this set is obtained. It is shown that, when $f(k) = k^α, k \ge 1,$ for any $α\in (0,1/2]$, this size grows at a smaller rate than any positive power of the network size.

math.PR↗