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We study the central limit theorem in the non-normal domain of attraction to symmetric $\alpha$-stable laws for $0<\alpha\leq2$. We show that for i.i.d. random variables $X_i$, the convergence rate in $L^\infty$ of both the densities and…

Probability · Mathematics 2018-04-24 Christoph Börgers , Claude Greengard

An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…

Disordered Systems and Neural Networks · Physics 2009-11-13 Paul E. Parris , Julián Candia , V. M. Kenkre

We consider two dimensional random walks conditioned to stay in the positive quadrant. Assuming that the increments of the walk have finite second moments and that the drift vector is co-oriented with one of two axes, we construct positive…

Probability · Mathematics 2026-02-10 Tuan Anh Nguyen , Vitali Wachtel

We consider a class of multi-particle reinforced interacting random walks. In this model, there are some (finite or infinite) particles performing random walks on a given (finite or infinite) connected graph, so that each particle has…

Probability · Mathematics 2013-03-26 Jun Chen

We study decentralized learning over networks where data are distributed across nodes without a central coordinator. Random walk learning is a token-based approach in which a single model is propagated across the network and updated at each…

Machine Learning · Computer Science 2026-04-15 Zonghong Liu , Matthew Dwyer , Salim El Rouayheb

We investigate macroscopic behavior of a dynamical network consisting of a time-evolving wiring of interactions among a group of random walkers. We assume that each walker (agent) has an oscillator and show that depending upon the nature of…

Chaotic Dynamics · Physics 2017-07-06 Soumen Majhi , Dibakar Ghosh

The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…

Quantum Physics · Physics 2013-05-29 Alex D. Gottlieb

We studied simple random-walk models with asymmetric time delays. Stochastic simulations were performed for hyperbolic-tangent fitness functions and to obtain analytical results we approximated them by step functions. A novel behavior has…

Statistical Mechanics · Physics 2025-05-30 Kamil Łopuszański , Jacek Miękisz

This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a function of its summands as their number tends to infinity. In the large deviation range of the…

Probability · Mathematics 2014-09-08 Michel Broniatowski , Virgile Caron

We prove CLTs for biased randomly trapped random walks in one dimension. In particular, we will establish an annealed invariance principal by considering a sequence of regeneration times under the assumption that the trapping times have…

Probability · Mathematics 2016-11-22 Adam Bowditch

We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…

Probability · Mathematics 2009-07-15 Olivier Raimond , Bruno Schapira

There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between…

Quantum Physics · Physics 2010-06-08 Norio Konno

We consider homogeneous open quantum random walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of the quantum trajectories of the walk. We prove that the properly rescaled position…

Probability · Mathematics 2022-06-08 Raffaella Carbone , Federico Girotti , Anderson Melchor Hernandez

In this paper, we extend the functional central limit theorems for the occupation times of the voter models on lattices given in Xue2026 to the case where the initial distribution is a spatially inhomogeneous product measure. The duality…

Probability · Mathematics 2026-03-10 Xiaofeng Xue

Consider a continuous time random walk in $\mathbb{Z}$ with independent and exponentially distributed jumps $\pm1$. The model in this paper consists in an infinite number of such random walks starting from the complement of…

Mathematical Physics · Physics 2013-07-25 Mark Adler , Patrik L. Ferrari , Pierre van Moerbeke

Based on a martingale theory approach, we present a complete characterization of the asymptotic behaviour of a lazy reinforced random walk (LRRW) which shows three different regimes (diffusive, critical and superdiffusive). This allows us…

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…

We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination…

Statistical Mechanics · Physics 2007-05-23 Jae Dong Noh , Heiko Rieger

We consider dynamic random walks where the nearest neighbour jump rates are determined by an underlying supercritical contact process in equilibrium. This has previously been studied by den Hollander and dos Santos and den Hollander, dos…

Probability · Mathematics 2014-10-30 Thomas Mountford , Maria E. Vares

In [3] the radius of convergence of the generating function of the collision local time of two independent copies of an irreducible, symmetric and transient random walk on Zd, d \geq 1, was studied. Two versions were considered: z1, the…

Probability · Mathematics 2012-06-11 Frank den Hollander , Alex A. Opoku