arXiv subjects

Sanchayan Bhowal

Publications and source records attributed to Sanchayan Bhowal.

6 recordsLinked to original sources

arXiv2026

Scaling Limits for Ising Models on Inhomogeneous Random Graphs and Applications

In this paper, we derive quenched scaling limits for linear functionals and the empirical spin field of Ising models on inhomogeneous random graphs generated by a graphon (encompassing both dense and sparse graphs), in the high-temperature regime. We first prove a joint central limit theorem (CLT) for finite collections of linear statistics of the spin configurations, where the limiting covariance is characterized by the resolvent of the associated graphon integral operator. Building on this result, we establish functional CLTs for the average magnetization and for the spin field indexed by suitable classes of regular test functions. We further prove convergence of the full empirical spin field, viewed as a random generalized function in negative Sobolev spaces. These scaling limits provide applications to both Bayesian neural networks and causal inference. Specifically, for the former, we derive infinite-width Gaussian-process limits for two-layer Bayesian neural networks with Ising-dependent output-layer signs, while for the latter, we establish the asymptotic normality of H\'{a}jek estimators for average treatment effects under network interference.

math.PR↗

arXiv2026

Ising Models on Inhomogeneous Random Graphs: Inference, Local Asymptotic Minimaxity, and Limit of Experiments

In this paper, we develop an inferential framework with sharp asymptotic optimality guarantees for Ising models on inhomogeneous random graphs in the subcritical parameter regime. We begin by characterizing the asymptotic distribution of the maximum likelihood (ML) estimate of the natural parameter, based on a single sample from the underlying model, covering both sparse and dense network regimes. Next, to overcome the computational intractability of the ML method, we propose a simple closed-form estimate obtained from a one-step approximation to the likelihood equation. We show that this estimate attains the same asymptotic distribution and variance as the ML estimate, thereby yielding a computationally efficient and asymptotically valid confidence interval for the natural parameter. We complement these inferential results by establishing a H\'ajek--Le Cam-type local asymptotic minimax theorem, showing that the proposed estimate achieves the smallest possible asymptotic maximum risk, both in rate and in leading constant, over shrinking neighborhoods of the true parameter. We also derive the corresponding limit of experiments. To the best of our knowledge, these are among the first sharp asymptotic optimality results for network-dependent data. Finally, we study goodness-of-fit testing for the natural parameter, deriving the local power of the likelihood ratio test and minimax detection rates. Our analysis relies on new fluctuation results for the sufficient statistic (Hamiltonian) and for the random partition function of Ising models on inhomogeneous random graphs, which are of independent interest.

math.ST↗

arXiv2025

Thresholds and Fluctuations of Submultiplexes in Random Multiplex Networks

In a multiplex network a common set of nodes is connected through different types of interactions, each represented as a separate graph (layer) within the network. In this paper, we study the asymptotic properties of submultiplexes, the counterparts of subgraphs (motifs) in single-layer networks, in the correlated Erd\H{o}s-R\'{e}nyi multiplex model. This is a random multiplex model with two layers, where the graphs in each layer marginally follow the classical (single-layer) Erd\H{o}s-R\'{e}nyi model, while the edges across layers are correlated. We derive the precise threshold condition for the emergence of a fixed submultiplex $\boldsymbol{H}$ in a random multiplex sampled from the correlated Erd\H{o}s-R\'{e}nyi model. Specifically, we show that the satisfiability region, the regime where the random multiplex contains infinitely many copies of $\boldsymbol{H}$, forms a polyhedral subset of $\mathbb{R}^3$. Furthermore, within this region the count of $\boldsymbol{H}$ is asymptotically normal, with an explicit convergence rate in the Wasserstein distance. We also establish various Poisson approximation results for the count of $\boldsymbol{H}$ on the boundary of the threshold, which depends on a notion of balance of submultiplexes. Collectively, these results provide an asymptotic theory for small submultiplexes in the correlated multiplex model, analogous to the classical theory of small subgraphs in random graphs.

math.PR↗

arXiv2024

Rates of Convergence of the Magnetization in the Tensor Curie-Weiss Potts Model

In this paper, we derive distributional convergence rates for the magnetization vector and the maximum pseudolikelihood estimator of the inverse temperature parameter in the tensor Curie-Weiss Potts model. Limit theorems for the magnetization vector have been derived recently in Bhowal and Mukherjee (2023), where several phase transition phenomena in terms of the scaling of the (centered) magnetization and its asymptotic distribution were established, depending upon the position of the true parameters in the parameter space. In the current work, we establish Berry-Esseen type results for the magnetization vector, specifying its rate of convergence at these different phases. At most points in the parameter space, this rate is $N^{-1/2}$ ($N$ being the size of the Curie-Weiss network), while at some "special" points, the rate is either $N^{-1/4}$ or $N^{-1/6}$, depending upon the behavior of the fourth derivative of a certain "negative free energy function" at these special points. These results are then used to derive Berry-Esseen type bounds for the maximum pseudolikelihood estimator of the inverse temperature parameter whenever it lies above a certain criticality threshold.

math.PR↗

arXiv2023

Limit Theorems and Phase Transitions in the Tensor Curie-Weiss Potts Model

In this paper, we derive results about the limiting distribution of the empirical magnetization vector and the maximum likelihood (ML) estimates of the natural parameters in the tensor Curie-Weiss Potts model. Our results reveal surprisingly new phase transition phenomena including the existence of a smooth curve in the interior of the parameter plane on which the magnetization vector and the ML estimates have mixture limiting distributions, the latter comprising of both continuous and discrete components, and a surprising superefficiency phenomenon of the ML estimates, which stipulates an $N^{-3/4}$ rate of convergence of the estimates to some non-Gaussian distribution at certain special points of one type and an $N^{-5/6}$ rate of convergence to some other non-Gaussian distribution at another special point of a different type. The last case can arise only for one particular value of the tuple of the tensor interaction order and the number of colors. These results are then used to derive asymptotic confidence intervals for the natural parameters at all points where consistent estimation is possible.

math.ST↗

arXiv2022

Optimizing the location of the colony of foragers with Collective Learning

Animal groups collaborate with one another throughout their lives to better comprehend their surroundings. Here, we try to model, using continuous random walks, how the entire process of birth, reproduction, and death might impact the searching process. We attempt to simulate an ecosystem where the post-reproductive foragers leave their colonies to discover where the targets are while others stay and breed at the base. Actually, a group of foragers searches for a location from where they access the targets for food supply. Particularly, we have explored a hypothetical situation in which the relocation to the new position depends on the agreement level of the species as well as an additional waiting time due to this agreement level. In this backdrop, detailed numerical results reveal that searching for an optimal position at an optimal mean time can be captured for a suitable range of the agreement level. We have also shown, for a given agreement level, the optimal mean time linearly increases with the Death-to-Birth ratio.

nlin.AO↗