Related papers: Large deviations of random walks on random graphs
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the…
Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and…
We study random walks on the integers driven by a sample of time-dependent nearest-neighbor conductances that are bounded but are permitted to vanish over time intervals of positive Lebesgue-length. Assuming only ergodicity of the…
In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…
Large deviation theory provides a framework to understand macroscopic fluctuations and collective phenomena in many-body nonequilibrium systems in terms of microscopic dynamics. In these lecture notes we discuss the large deviation…
We consider a discrete-time continuous-space random walk under the constraints that the number of returns to the origin (local time) and the total area under the walk are fixed. We first compute the joint probability of an excursion having…
Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…
Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the…
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…
We examine a new path transform on 1-dimensional simple random walks and Brownian motion, the quantile transform. This transformation relates to identities in fluctuation theory due to Wendel, Port, Dassios and others, and to discrete and…
Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision…
The process of fluctuations of trajectory observables of stochastic systems is related to processes with independent increments from the risk theory. The first-passage times of variables of the thermodynamics of trajectories, in particular,…
We introduce a general model of trapping for random walks on graphs. We give the possible scaling limits of these Randomly Trapped Random Walks on $\mathbb {Z}$. These scaling limits include the well-known fractional kinetics process, the…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
In this paper we study the behavior of a continuous time random walk (CTRW) on a stationary and ergodic time varying dynamic graph. We establish conditions under which the CTRW is a stationary and ergodic process. In general, the stationary…
For a multivariate random walk with i.i.d. jumps satisfying the Cramer moment condition and having a mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant…
We study the fluctuations of systems modeled by Markov jump processes with periodic generators. We focus on observables defined through time-periodic functions of the system's states or transitions. Using large deviation theory, canonical…