arXiv subjects

Tamojit Sadhukhan

Publications and source records attributed to Tamojit Sadhukhan.

4 recordsLinked to original sources

arXiv2026

Asymptotic Properties of Generalized Elephant Random Walks

Elephant random walk is a special type of random walk that incorporates the memory of the past to determine its future steps. The probability of this walk taking a particular step (+1 or -1) at a time point, conditioned on the entire history, depends on a linear function of the proportion of steps of that type till that time point. In this work, we consider a generalization of the elephant random walk where we investigate how the dynamics of the random walk will change if we replace this linear function with a generic map satisfying some analytic conditions. We propose a new model, called the multidimensional generalized elephant random walk, that includes several variants of elephant random walk in one and higher dimensions and generalizations thereof. Using tools from the theory of stochastic approximation, we derive the asymptotic behavior of our model leading to newer results on the phase transition boundary between diffusive and non-diffusive regimes. In the process, we extend some results on one-dimensional stochastic approximation process, which can be of independent interest. We also mention a few open problems in this context.

math.PR↗

arXiv2026

A Statistical Framework for Learning Preferences from the Past

In many real-world settings such as online recommendation or consumer choice modeling, individuals make repeated choices from a fixed set of options. Accurately estimating their underlying preferences is essential for generating personalized future recommendations. Probabilistic models for understanding user choice behavior from past decisions can serve as a valuable addition to existing recommender systems and choice prediction methods. To this end, in this article, we introduce a novel statistical framework for predicting user preferences based on their past choices, under a natural monotonicity assumption: options that were chosen more frequently or more intensely in the past are more likely to be chosen again in the future. Our approach builds on a parametric model proposed by Le Goff and Soulier (2017), originally used to describe how ants in an ant colony select a path among many pre-existing paths. We propose a non-parametric generalization of this model, drawing inspiration from the generalized elephant random walk introduced by Maulik et al. (2024). We develop a method of maximum likelihood estimation of the user preference probabilities under the above-mentioned monotonicity constraint. We also derive theoretical guarantees for our estimator and demonstrate the effectiveness of our method through both simulated experiments and real-world datasets.

stat.ME↗

arXiv2025

Phase Transitions for Elephant Random Walks with Two memory Channels

Elephant random walk, introduced to study the effect of memory on random walks, is a novel type of walk that incorporates the information of one randomly chosen past step to determine the future step. However, memory of a process can be multifaceted and can arise due to interactions of more than one underlying phenomena. To model this, random walks with multiple memory channels were introduced in the statistical physics literature by Saha (2022) - here the information on a bunch of independently chosen past steps is needed to decide the future step. With the help of variance heuristics, this work analyzed the two-channel case and predicted a double phase transition: from diffusive to superdiffusive and from superdiffusive to ballistic regimes. We prove these conjectures rigorously (with some corrections), discover a mildly superdiffusive regime at one of the conjectured transition boundaries, and observe a new second-order phase transition. We also carry out a detailed investigation of the asymptotic behavior of the walk at different regimes.

math.PR↗

arXiv2023

A dynamic mean-field statistical model of academic collaboration

There is empirical evidence that collaboration in academia has increased significantly during the past few decades, perhaps due to the breathtaking advancements in communication and technology during this period. Multi-author articles have become more frequent than single-author ones. Interdisciplinary collaboration is also on the rise. Although there have been several studies on the dynamical aspects of collaboration networks, systematic statistical models which theoretically explain various empirically observed features of such networks have been lacking. In this work, we propose a dynamic mean-field model and an associated estimation framework for academic collaboration networks. We primarily focus on how the degree of collaboration of a typical author, rather than the local structure of her collaboration network, changes over time. We consider several popular indices of collaboration from the literature and study their dynamics under the proposed model. In particular, we obtain exact formulae for the expectations and temporal rates of change of these indices. Through extensive simulation experiments, we demonstrate that the proposed model has enough flexibility to capture various phenomena characteristic of real-world collaboration networks. Using metadata on papers from the arXiv repository, we empirically study the mean-field collaboration dynamics in disciplines such as Computer Science, Mathematics and Physics.

stat.ME↗