arXiv subjects

Ayan Ghosh

Publications and source records attributed to Ayan Ghosh.

15 recordsLinked to original sources

arXiv2026

Statistically characterized subgroups related to arithmetic-type sequence of integers

Very recently, in [Das et al., J. Lond. Math. Soc., 2025], statistically characterized subgroups were studied for certain classes of non-arithmetic sequences. Subsequently, in [Das et al., Bull. Sci. Math., 2025], characterized subgroups were investigated for a class of arithmetic-type sequences that includes both arithmetic sequences and certain non-arithmetic sequences. Motivated by these developments, we study statistically characterized subgroups associated with a broader class of arithmetic-type sequences. In particular, all previously obtained cardinality related observations for statistically characterized subgroups corresponding to arithmetic sequences as well as certain non-arithmetic sequences follow as special cases of our results. Moreover, we show that this broader class exhibits drastically different behavior and differs significantly from the previously studied special cases.

math.GR↗

arXiv2026

Ergodic Theorems for Random Walks in Random Environments

We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to first prove a uniqueness principle. We use a more general definition of environments using~\textit{Environment Functions}. As a corollary, we can deduce an invariance principle under these assumptions for balanced environments under some assumptions. We also use the uniqueness principle to show that any balanced, elliptic random walk must have the same transience behaviour as the simple symmetric random walk. The second is to transfer the results we deduce in balanced environments to general ergodic environments(under some assumptions) using a control technique to derive a measure under which the \textit{local process} is stationary and ergodic. As a consequence of our results, we deduce the Law of Large Numbers for the Random Walk and an Invariance Principle under our assumptions.

math.PR↗

arXiv2025

Characterizing infinite torsion subgroups of the circle through arithmetic-type sequences

In a recent work [Das et al., Bull. Sci. Math. 199 (2025), 103580], the structure of characterized subgroups corresponding to arithmetic-type sequences was investigated. Building upon this work, we further show that a characterized subgroup associated with an arithmetic-type sequence is countable if and only if it is torsion. Further we prove that any infinite torsion subgroup of the circle can be characterized by an arithmetic-type sequence with bounded ratio. Moreover, our findings demonstrate that the dichotomy observed in Eggleston's theorem [Theorem 16, Eggleston, Proc. Lond. Math. Soc. 54(2) (1952), 42--93] for arithmetic sequences does not extend, in general, to the broader class of arithmetic-type sequences.

math.NT↗

arXiv2025

Resistance hysteresis in twisted bilayer graphene: Intrinsic versus extrinsic effects

Hysteresis in resistance under magnetic field sweeps is a key signature for identifying magnetism in twisted bilayer graphene and similar systems. However, such sweeps can induce extrinsic thermal effects, complicating interpretations. Distinguishing intrinsic magnetic ordering from extrinsic thermal influences is crucial. In this study, we report hysteresis in the longitudinal resistance ($(R_{xx}$)) of a near magic-angle twisted bilayer graphene (TBG) sample under an in-plane magnetic field ($(B_{||}$)). The hysteresis phase appears at the edge of the superconducting dome, diminishes deep within the superconducting regime, and reemerges near the superconducting critical temperature ($(T \sim T_c$)). The hysteresis magnitude and coercive fields strongly depend on the magnetic field sweep rate ($(dB/dt)$) and exhibit transient relaxation in time-series measurements. Notably, similar hysteresis behavior was observed in the temperature profile of the sample stage, measured using a calibrated temperature sensor under analogous magnetic field cycles, suggesting extrinsic thermal origins rather than intrinsic magnetic ordering. These findings underscore the importance of carefully distinguishing intrinsic and extrinsic effects in resistance hysteresis observed in mesoscopic van der Waals systems.

cond-mat.mes-hall↗

arXiv2025

Statistically characterized subgroups related to some non-arithmetic sequence of integers II (a quest for countable subgroups)

Following the work of [Dikranjan et al., Fund. Math. 249:185-209, 2020] for arithmetic sequences, very recently in [Das et al., Expo. Math. 43(3):125653, 2025], statistically characterized subgroups have been investigated for certain types of non-arithmetic sequences. Building on this work, we investigate further and demonstrate that, for a particular class of non-arithmetic sequences, the statistically characterized subgroup coincides with the corresponding characterized subgroup. In this context it should be kept in mind that statistical convergence (convergence w.r. to the ideal of natural density zero sets) encompasses much more sequences than usual convergence (convergence w.r. to the ideal of finite sets) and it had already been shown that statistically characterized subgroups corresponding to arithmetic sequences can not be characterized by any sequence [Das et al., Bull. Sci. Math. 179(2):103157, 2022] and they are always of the size of the continuum. From the very beginning it has been an open question as to whether statistically characterized subgroups can be small in size i.e. countably infinite. Our observation thus sheds new light on the crucial role of sequences generating subgroups of the circle group and at the same time one can subsequently identify a class of sequences for which statistically characterized subgroups are countably infinite. This result provides a negative solution to Problem 2.16 posed in [Das et al., Expo. Math. 43(3):125653, 2025] and Question 6.3 from [Dikranjan et al., Fund. Math. 249:185-209, 2020]. Additionally, our findings resolve several open problems from [Dikranjan et al., Topo. Appl., 2025].

math.GN↗

arXiv2024

Statistically characterized subgroups related to some non-arithmetic sequence of integers

Recently, in Das et al. (Mediterr. J. Math. 21 : 164, 2024), characterized subgroups are investigated for some special kind of non-arithmetic sequences. In this note, we study subsequent problems in case of ``statistically characterized subgroups" introduced in Dikranjan et al. (Fund. Math. 249 : 185-209, 2020). The entire investigation emphasizes that these statistically characterized subgroups are mostly larger in size, having cardinality $\mathfrak{c}$, and exhibit behavior that significantly differs from that of classically characterized subgroups. As a consequence, we solve an open problem raised in Dikranjan et al. (Fund. Math. 249 : 185-209, 2020).

math.GR↗

arXiv2024

Thermopower probing emergent local moments in magic-angle twisted bilayer graphene

Recent experiments on magic-angle twisted bilayer graphene (MATBLG) have revealed the formation of flatbands, suggesting that correlation effects are likely to dominate in this system. Yet, a global transport measurement showing distinct signatures of strong correlations like local moments arising from the flatbands is missing. Utilizing thermopower as a sensitive global transport probe for measuring entropy, we unveil the presence of emergent local moments through their impact on entropy. Remarkably, in addition to sign changes at the Dirac point ($\nu = 0$) and full band filling ($\nu = \pm 4$), the thermopower of MATBLG demonstrates additional sign changes at the location, $\nu_{cross} \sim \pm 1$, which do not vary with temperature from $5K$ to $\sim 60K$. This is in contrast to sensitive temperature-dependent crossing points seen in our study on twisted bilayer graphene devices with weaker correlations. Further, we have investigated the effect of magnetic field ($B$) on the thermopower, both $B_{\parallel}$ and $B_{\perp}$. Our results show a $30\%$ and $50\%$ reduction, respectively, that is consistent with suppression seen in the layered oxide due to the partial polarization of the spin entropy. The observed robust crossing points, together with suppression in a magnetic field, cannot be explained solely from the contributions of band fermions; instead, our data is consistent with the dominant contribution arising from the entropy of the emergent localized moments of a strongly correlated flatband.

cond-mat.mes-hall↗

arXiv2024

Electric field tunable superconductivity with competing orders in twisted bilayer graphene near magic-angle

Superconductivity (SC) in twisted bilayer graphene (tBLG) has been explored by varying carrier concentrations, twist angles, and screening strength, with the aim of uncovering its origin and possible connections to strong electronic correlations in narrow bands and various resulting broken symmetries. However, the link between the tBLG band structure and the onset of SC and other orders largely remains unclear. In this study, we address this crucial gap by examining in-situ band structure tuning of a near magic-angle ($\theta \approx0.95^\circ$) tBLG device with displacement field ($D$) and reveal remarkable competition between SC and other broken symmetries. At zero $D$, the device exhibits superconducting signatures without the resistance peak at half-filling, a characteristic signature with a strong electronic correlation. As $D$ increases, the SC is suppressed, accompanied by the appearance of a resistance peak at half-filling. Hall density measurements reveal that at zero $D$, SC arises around the van Hove singularity (vHs) from an isospin or spin-valley unpolarized band. At higher $D$, the suppression of SC coincides with broken isospin symmetry near half-filling with lifted degeneracy ($g_d \sim 2$). Additionally, as the SC phase becomes weaker with $D$, vHs shifts to higher fillings, highlighting the modification of the underlying band structure with the applied electric field. These findings, with recent theoretical study on SC in tBLG, highlight the competition, rather being connected concomitantly, between SC and other orders promoted by broken symmetries.

cond-mat.mes-hall↗

arXiv2024

When ideals properly extend the class of Arbault sets

In this article we continue the investigation of generalized version of Arbault sets, that was initiated in [Das et al., Bul. Sci. Math. 179 (2022), 103157] but look at the picture from the most general point of view where ideals come into play. While Arbault sets can be naturally associated with the Frechet ideal $Fin$, in [Das et al., Bul. Sci. Math. 179 (2022), 103157] it was observed that when $Fin$ is replaced by the natural density ideal $\iI_d$ one can obtain a strictly larger class of trigonometric thin sets containing Arbault sets. From the set theoretic point of view a natural question arises as to whether one can broaden the picture and specify a class of ideals (instead of a single ideal) each of which would have the similar effect on the classical notion. As a natural candidate, we focus on a special class of ideals, namely, non-$snt$ ideals with a specific property ($snt$ stands for ``strongly non translation invariant"). This class happens to be quite large and rich as it properly contains the class of all dense translation invariant ideals ($\varsupsetneq Fin$), ideals generated by simple density functions as also certain non-negative regular summability matrices (but not all) which can be seen from [Das et al., Annals of Pure and Applied Logic 174 (2023), 103289]. We consider the resulting class of $\iI$-Arbault sets and it is observed that for each such ideal, the class of $\iI$-Arbault sets not only properly contains the class of classical Arbault sets but also a large subfamily of $\NN$-sets (also called ``sets of absolute convergence") while being contained in the class of weak Dirichlet sets.

math.GN↗

arXiv2022

Excitonic Metal and Non-Fermi Liquid Behaviour in Twisted Double Bilayer Graphene near Charge Neutrality

Twisted double bilayer graphene is a compensated semi-metal near the charge neutrality point with the presence of small electron and hole pockets in its band structure. We show that strong Coulomb attraction between the electrons and holes can lead to the formation of indirect excitons. Condensation of these excitons at low temperature creates an excitonic metal with charge density wave order for an appropriate range of interaction strength. This has interesting implications for low-temperature transport in the system as a function of carrier density and temperature. The reorganization of the single particle excitations and their density of states in the excitonic metal can lead to peaks in resistivity as a function of carrier density, recently seen in experiments at low temperatures. The fluctuations of the Landau damped order parameter in the quantum critical metal lead to non-Fermi liquid behaviour, which can explain the sublinear $T^{2/3}$ dependence of the resistance near the charge neutrality point.

cond-mat.str-el↗

arXiv2022

Evidence of a compensated semimetal with electronic correlations at the CNP of twisted double bilayer graphene

Recently, magic-angle twisted bilayer graphene (MATBLG) has shown the emergence of various interaction-driven novel quantum phases at the commensurate fillings of the moir'e superlattice, while the charge neutrality point (CNP) remains mostly a vanilla insulator. Here, we show an emerging phase of nearly compensated semimetallicity at the CNP of twisted double bilayer graphene (TDBLG), a close cousin of MATBLG, with signatures of electronic correlation. Using electrical and thermal transport, we find almost two orders of magnitude enhancement of the thermopower in magnetic fields much smaller than the extreme quantum limit, accompanied by a large magnetoresistance($\sim 2500\%$) at CNP. This provides indisputable experimental evidence that TDBLG near CNP is a compensated semimetal. Moreover, at low temperatures, we observe an unusual sublinear temperature dependence of resistance. A recent theory predicts the formation of an excitonic metal near CNP, where small electron and hole pockets coexist. We understand the sublinear temperature dependence in terms of critical fluctuations in this theory.

cond-mat.mes-hall↗

arXiv2021

Interaction driven giant thermopower in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene (MtBLG) has proven to be an extremely promising new platform to realize and study a host of emergent quantum phases arising from the strong correlations in its narrow bandwidth flat band. In this regard, thermal transport phenomena like thermopower, in addition to being coveted technologically, is also sensitive to the particle-hole (PH) asymmetry, making it a crucial tool to probe the underlying electronic structure of this material. We have carried out thermopower measurements of MtBLG as a function of carrier density, temperature and magnetic field, and report the observation of an unusually large thermopower reaching up to a value as high as $\sim \bf{100μV/K}$ at a low temperature of 1K. Surprisingly, our observed thermopower exhibiting peak-like features in close correspondence to the resistance peaks around the integer Moire fillings, including the Dirac Point, violating the Mott formula. %Surprisingly, our observed thermopower exhibits peak-like features in close correspondence to the resistance peaks around the integer Moire fillings, including the Dirac Point, which completely violates the Mott formula. We show that the large thermopower peaks and their %non-monotonic dependence with temperature and magnetic field associated behaviour arise from the emergent highly PH asymmetric electronic structure due to the cascade of Dirac revivals. Furthermore, the thermopower shows an anomalous peak around the superconducting transition on the hole side and points towards the possible role of enhanced superconducting fluctuations in MtBLG.

cond-mat.mes-hall↗

arXiv2021

Recommending Insurance products by using Users' Sentiments

In today's tech-savvy world every industry is trying to formulate methods for recommending products by combining several techniques and algorithms to form a pool that would bring forward the most enhanced models for making the predictions. Building on these lines is our paper focused on the application of sentiment analysis for recommendation in the insurance domain. We tried building the following Machine Learning models namely, Logistic Regression, Multinomial Naive Bayes, and the mighty Random Forest for analyzing the polarity of a given feedback line given by a customer. Then we used this polarity along with other attributes like Age, Gender, Locality, Income, and the list of other products already purchased by our existing customers as input for our recommendation model. Then we matched the polarity score along with the user's profiles and generated the list of insurance products to be recommended in descending order. Despite our model's simplicity and the lack of the key data sets, the results seemed very logical and realistic. So, by developing the model with more enhanced methods and with access to better and true data gathered from an insurance industry may be the sector could be very well benefitted from the amalgamation of sentiment analysis with a recommendation.

cs.IR↗

arXiv2020

Generating Subgroups of the Circle using a Generalized class of Density Functions

In this article, we consider the generalized version $d^f_g$ of the natural density function introduced in \cite{BDK} where $g : \N \rightarrow [0,\infty)$ satisfies $g(n) \rightarrow \infty$ and $\frac{n}{g(n)} \nrightarrow 0$ whereas $f$ is an unbounded modulus function and generate versions of characterized subgroups of the circle group $\T$ using these density functions. We show that these subgroups have the same feature as the $s$-characterized subgroups \cite{DDB} or $α$-characterized subgroups \cite{BDH} and our results provide more general versions of the main results of both the articles. But at the same time the utility of this more general approach is justified by constructing new and nontrivial subgroups for suitable choice of $f$ and $g$. In several of our results we use properties of the ideal $\iZ_g(f)$ which are first presented along with certain new observations about these ideals which were not there in \cite{BDK}.

math.GN↗

arXiv2020

Topological torsion elements via natural density and a quest for solution of Armacost like problem

One can use the number theoretic idea of the notion of natural density \cite{B1} to define topological s-torsion elements (which form the statistically characterized subgroups, recently developed in \cite{DPK}) extending Armacost's idea of topological torsion elements. We follow in the line of Armacost who had posed the famous classical problem for "description of topological torsion elements" of the circle group. In this note we consider the natural density version of Armacost's problem and present a complete description of topological s-torsion elements in terms of the support, for all arithmetic sequences which also provides the solution of Problem 6.10 posed in \cite{DPK} .

math.GN↗