Related papers: Fluctuation theory for Markov random walks

We exhibit the invariance of cycle affinities in finite state Markov processes under various natural probabilistic constructions, for instance under conditioning and under a new combinatorial construction that we call ``drag and drop''. We…

We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in…

The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking…

Consider the random walk $G_n : = g_n \ldots g_1$, $n \geq 1$, where $(g_n)_{n\geq 1}$ is a sequence of independent and identically distributed random elements with law $\mu$ on the general linear group ${\rm GL}(V)$ with $V=\mathbb R^d$.…

The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of…

Let $h:[0,1]\to\mathbb{R}$ be $C^2$ and such that $\sup_{[0,1]} h''<0$. For a (large) positive integer $n$, set $h_n(k) = n h(k/n)$ for any $k\in\{0,\dots,n\}$. We consider a random walk $(S_k)_{k\geq 0}$ with i.i.d.\ centred increments…

We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…

First passage time plays a fundamental role in dynamical characterization of stochastic processes. Crucially, our current understanding on the problem is almost entirely relies on the theoretical formulations, which assume the processes…

Extensive empirical investigation has shown that a plethora of real networks synchronously exhibit scale-free and modular structure, and it is thus of great importance to uncover the effects of these two striking properties on various…

In this paper we consider a particular version of the random walk with restarts: random reset events which bring suddenly the system to the starting value. We analyze its relevant statistical properties like the transition probability and…

We propose an intermediate walk continuously connecting an open quantum random walk and a quantum walk with parameters $M\in \mathbb{N}$ controlling a decoherence effect; if $M=1$, the walk coincides with an open quantum random walk, while…

Multivariate fluctuation relations are established in three stochastic models of transistors, which are electronic devices with three ports and thus two coupled currents. In the first model, the transistor has no internal state variable and…

We consider a system of $N$ identical independent Markov processes, each taking values 0 or 1. The system describes a stochastic dynamics of an ensemble of two-level atoms. The atoms are exposed to a photon flux. Under the photon flux…

We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…

The main goal of this text is comprehensive study of time homogeneous Markov chains on the real line whose drift tends to zero at infinity, we call such processes Markov chains with asymptotically zero drift. Traditionally this topic is…

For an arbitrary transient random walk $(S_n)_{n\ge 0}$ in $\mathbb Z^d$, $d\ge 1$, we prove a strong law of large numbers for the spatial sum $\sum_{x\in\mathbb Z^d}f(l(n,x))$ of a function $f$ of the local times…

We consider the simple random walk on Z^d evolving in a potential of independent and identically distributed random variables taking values in [0, + \infty]. We give optimal conditions for the existence of the quenched point-to-point…

In the eighties, A. Connes and E. J. Woods made a connection between hyperfinite von Neumann algebras and Poisson boundaries of time dependent random walks. The present paper explains this connection and gives a detailed proof of two…

In the last few decades, noise-induced large fluctuations and transition phenomena have garnered significant attention in a variety of scientific contexts. The concept of prehistory probability has been proposed within the framework of…

In 2008, T\'oth and Vet\H{o} defined the self-repelling random walk with directed edges as a non-Markovian random walk on $\mathbb{Z}$: in this model, the probability that the walk moves from a point of $\mathbb{Z}$ to a given neighbor…