About

Sayan Banerjee is an Associate Professor in the Department of Statistics and Operations Research at the University of North Carolina, Chapel Hill. He obtained his undergraduate and master's education at the Indian Statistical Institute in Kolkata from 2005 to 2010, and completed his Ph.D. in mathematics at the University of Washington, Seattle, in 2013, advised by Professor Krzysztof Burdzy. He was a Research Fellow in the Statistics Department at the University of Warwick, UK, from November 2013 to June 2016, working with Professor Wilfrid Kendall, before joining UNC. His research focuses on probability theory and its applications. His recent work has been on coupling, geometry, and ergodicity of diffusion processes, dynamic random networks, and interacting particle systems. He has also worked on topics such as random walks in random environments and random matrices. In addition to his academic pursuits, he enjoys spending his spare time hanging out in coffee shops with friends, playing guitar, or binge-watching TV series on Netflix.

Research topics

• Computer Science
• Mathematics
• Mathematical analysis
• Statistics
• Statistical physics
• Data Mining
• Applied mathematics
• Combinatorics
• Physics
• Theoretical computer science
• Mathematical optimization
• Pure mathematics

Selected publications

• Rank Based Routing in Large Server Systems under Extreme Congestion

  ArXiv.org · 2026-05-17

  articleOpen access1st authorCorresponding

  We study $n$ parallel queues in an extreme heavy-traffic regime: each server works at rate $n$, while jobs arrive to a dispatcher at rate $n^2-(a-b)\sqrt{n}$, with fixed $a>b>0$. Arrivals are routed by a marginal join-the-shortest-queue policy: a small stream of rate $b\sqrt{n}$ joins the current shortest queue, while the remaining stream of rate $n^2-a\sqrt{n}$ is routed uniformly at random. This policy greatly reduces communication cost relative to full JSQ, while improving load balancing and offering a natural mechanism for premium jobs to join shorter queues. Under diffusive scaling, we prove limit theorems for the ranked queue lengths and associated gap process. The limit is an infinite-dimensional reflected Atlas process, with reflection at the origin and rank-based drift acting on the lowest particle. Its dynamics depend only on $b$, the shortest-queue arrival rate, while $a$ enters through the choice of invariant distribution. We prove well-posedness of this reflected infinite Atlas model and characterize a one-parameter family of product-form stationary gap distributions, parametrized by $a$ and $b$. To connect the diffusion limit with the stationary behavior of the queueing system, we introduce a related "system with pauses'' that agrees with the original dynamics at diffusion scale but admits an exact open Jackson network representation. This yields explicit finite-$n$ stationary gap distributions, whose heavy-traffic limits select the corresponding product-form invariant laws of the infinite reflected Atlas process. As consequences, we obtain sharp asymptotics for the lowest-ranked queues, system imbalance, and average queue length, quantifying the tradeoff between communication cost and load-balancing performance relative to random routing and full join-the-shortest-queue policies.

  PublisherOA PDF

• Rank Based Routing in Large Server Systems under Extreme Congestion

  arXiv (Cornell University) · 2026-05-17

  preprintOpen access1st authorCorresponding

  We study $n$ parallel queues in an extreme heavy-traffic regime: each server works at rate $n$, while jobs arrive to a dispatcher at rate $n^2-(a-b)\sqrt{n}$, with fixed $a>b>0$. Arrivals are routed by a marginal join-the-shortest-queue policy: a small stream of rate $b\sqrt{n}$ joins the current shortest queue, while the remaining stream of rate $n^2-a\sqrt{n}$ is routed uniformly at random. This policy greatly reduces communication cost relative to full JSQ, while improving load balancing and offering a natural mechanism for premium jobs to join shorter queues. Under diffusive scaling, we prove limit theorems for the ranked queue lengths and associated gap process. The limit is an infinite-dimensional reflected Atlas process, with reflection at the origin and rank-based drift acting on the lowest particle. Its dynamics depend only on $b$, the shortest-queue arrival rate, while $a$ enters through the choice of invariant distribution. We prove well-posedness of this reflected infinite Atlas model and characterize a one-parameter family of product-form stationary gap distributions, parametrized by $a$ and $b$. To connect the diffusion limit with the stationary behavior of the queueing system, we introduce a related "system with pauses'' that agrees with the original dynamics at diffusion scale but admits an exact open Jackson network representation. This yields explicit finite-$n$ stationary gap distributions, whose heavy-traffic limits select the corresponding product-form invariant laws of the infinite reflected Atlas process. As consequences, we obtain sharp asymptotics for the lowest-ranked queues, system imbalance, and average queue length, quantifying the tradeoff between communication cost and load-balancing performance relative to random routing and full join-the-shortest-queue policies.

  PublisherDOI

• Fluctuations of the Atlas model from inhomogeneous stationary profiles

  The Annals of Probability · 2026-04-21

  preprintOpen access1st authorCorresponding

  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 $t\to \infty$.

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• The past, present, and future of service recovery: a bibliometric analysis

  International Journal of Services and Operations Management · 2026-01-01

  article1st authorCorresponding
  PublisherDOI

• Load Balancing in Parallel Queues and Rank-Based Diffusions

  Mathematics of Operations Research · 2025-05-27 · 2 citations

  article1st authorCorresponding

  Consider a queuing 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 [Formula: see text], where [Formula: see text] and n is large. Interarrival and service times are taken to be independent and exponentially distributed. It is well known that the join-the-shortest-queue (JSQ) policy has many desirable load-balancing properties. In particular, in comparison with uniformly at random routing, the time asymptotic total queue-length of a JSQ system, in the heavy traffic limit, is reduced by a factor of K. However, this decrease in total queue-length comes at the price of a high communication cost of order [Formula: see text] because at each arrival instant, the state of the full K-dimensional system needs to be queried. In view of this, it is of interest to study alternative routing policies that have lower communication costs and yet have similar load-balancing properties as JSQ. In this work, we study a family of such rank-based routing policies, which we will call Marginal Size Bias Load-Balancing policies, in which [Formula: see text] 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 of such routing schemes, referred to as the marginal JSQ (MJSQ) policy, is one in which all the [Formula: see text] jobs are routed using the JSQ policy. Our first result provides a heavy traffic approximation theorem for such queuing systems in terms of reflected diffusions in the positive orthant [Formula: see text]. It turns out that, unlike the JSQ system, where, due to a state space collapse, the heavy traffic limit is characterized by a one-dimensional reflected Brownian motion, in the setting of MJSQ (and for the more general rank-based routing schemes), there is no state space collapse, and one obtains a novel diffusion limit which is the constrained analogue of the well-studied Atlas model (and other rank-based diffusions) that arise from certain problems in mathematical finance. Next, we prove an interchange of limits ([Formula: see text] and [Formula: see text]) result which shows that, under conditions, the steady state of the queuing system is well approximated by that of the limiting diffusion. It turns out that the latter steady state can be given explicitly in terms of product laws of Exponential random variables. Using these explicit formulae, and the interchange of limits result, 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 [Formula: see text], the steady-state heavy traffic total queue-length increases by at most a constant factor (independent of n, K) which can be made arbitrarily close to one by increasing a MJSQ parameter. We also study the case where the system is overloaded—namely, [Formula: see text]. For this case, we show that although the K-dimensional MJSQ system is unstable, unlike the setting of random routing, the system has certain desirable and quantifiable load-balancing properties. In particular, by establishing a suitable interchange of limits result, we show that the steady-state difference between the maximum and the minimum queue lengths stays bounded in probability (in the heavy traffic parameter n). Funding: Financial support from the National Science Foundation [RTG Award DMS-2134107] is gratefully acknowledged. S. Banerjee received financial support from the National Science Foundation [NSF-CAREER Award DMS-2141621]. A. Budhiraja received financial support from the National Science Foundation [Grant DMS-2152577].

  PublisherDOI

• Strong existence, pathwise uniqueness and chains of collisions in infinite Brownian particle systems

  ArXiv.org · 2025-01-14

  preprintOpen access1st authorCorresponding

  We study strong existence and pathwise uniqueness for a class of infinite-dimensional singular stochastic differential equations (SDE), with state space as the cone $\{x \in \mathbb{R}^{\mathbb{N}}: -\infty < x_1 \leq x_2 \leq \cdots\}$, referred to as an infinite system of competing Brownian particles. A `mass' parameter $p \in [0,1]$ governs the splitting proportions of the singular collision local time between adjacent state coordinates. Solutions in the case $p=1/2$ correspond to the well-studied rank-based diffusions, while the general case arises from scaling limits of interacting particle systems on the lattice with asymmetric interactions and the study of the KPZ equation. Under conditions on the initial configuration, the drift vector, and the growth of the local time terms, we establish pathwise uniqueness and strong existence of solutions to the SDE. A key observation is the connection between pathwise uniqueness and the finiteness of `chains of collisions' between adjacent particles influencing a tagged particle in the system. Ingredients in the proofs include classical comparison and monotonicity arguments for reflected Brownian motions, techniques from Brownian last-passage percolation, large deviation bounds for random matrix eigenvalues, and concentration estimates for extrema of Gaussian processes.

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

  arXiv (Cornell University) · 2025-01-02

  preprintOpen access1st authorCorresponding

  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.

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

  ArXiv.org · 2025-10-23

  preprintOpen access

  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.

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• Network Evolution With Mesoscopic Delays

  Random Structures and Algorithms · 2025-09-01 · 1 citations

  articleOpen access1st author

  ABSTRACT 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 (Banerjee et al. 2024) explores the regime of macroscopic delays in the evolution of the network.

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• D2C-WEBCRED

  International Journal of Electronic Commerce Studies · 2025-01-07 · 1 citations

  articleOpen access1st authorCorresponding

  Despite the fact that product and purchase related information on websites are one of the predominant factors in consumers’ decision-making processes to choose the right product, there exists limited research studies that assess the reliability of these information sources. Hence, this study is aimed at developing a multidimensional scale for assessing the credibility of direct-to-consumer (D2C) brand websites using source credibility theory. This study utilized a mixed-methods approach, including a comprehensive literature review, qualitative interviews with experts and consumers, and quantitative data analysis. The findings of the study supports the development of a new scale consisting of three dimensions viz., information precision, responsiveness, and usability experience to measure website credibility. Each dimension consisted of several items that were assessed using a 5-point Likert scale. The scale’s psychometric properties were examined through exploratory and confirmatory factor analysis, and the results indicated high levels of reliability and validity.

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Frequent coauthors

• Amarjit Budhiraja

  18 shared

• Shankar Bhamidi

  16 shared

• Wilfrid S. Kendall

  University of Warwick

  6 shared

• Krzysztof Burdzy

  6 shared

• Mariana Olvera‐Cravioto

  5 shared

• Brendan Brown

  Hudson Institute

  5 shared

• Dinesh Kumar Srivastava

  4 shared

• Xiangying Huang

  University of North Carolina at Chapel Hill

  4 shared