Related papers: Diffusive transport on networks with stochastic re…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
In this paper, we analyze the mean first passage time (MFPT) for a single Brownian particle to find a stochastically-gated target under the additional condition that the position of the particle is reset to a fixed position $\x_r$ at a rate…
This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks are characterized by the fact that the one-step transition probabilities are functions of the…
We perform a thorough analysis of the survival probability of symmetric random walks with stochastic resetting, defined as the probability for the walker not to cross the origin up to time $n$. For continuous symmetric distributions of step…
Stochastic networks based on random point sets as nodes have attracted considerable interest in many applications, particularly in communication networks, including wireless sensor networks, peer-to-peer networks and so on. The study of…
We introduce a general framework, applicable to a broad class of random walks on networks, that quantifies the response of the mean first-passage time to a target node to a local perturbation of the network, both in the context of attacks…
Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a time-independent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and…
We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
This paper studies the network throughput and transport delay of a multihop wireless random access network based on a Markov renewal model of packet transportation. We show that the distribution of the source-to-destination (SD) distance…
Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and…
A second-order random walk on a graph or network is a random walk where transition probabilities depend not only on the present node but also on the previous one. A notable example is the non-backtracking random walk, where the walker is…
We investigate the statistics of fluctuations in a classical stochastic network of nodes joined by connectors. The nodes carry generalized charge that may be randomly transferred from one node to another. Our goal is to find the time…
We study first-passage time problems for a diffusive particle with stochastic resetting with a finite rate $r$. The optimal search time is compared quantitatively with that of an effective equilibrium Langevin process with the same…
In this paper we present a combinatorial optimisation view on the routing problem for connectionless packet networks by using the metaphor of a landscape. We examine the main properties of the routing landscapes as we define them and how…
Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.…
In this paper, we conduct a literature review of laws of motion based on stochastic search strategies which are mainly focused on exploring highly dynamic environments. In this regard, stochastic search strategies represent an interesting…
We consider random walks that start and are absorbed on the leaves of random networks and study the length of such walks. For the networks we investigate, Erdos-Renyi random graphs and Barabasi-Albert scale free networks, these walks are…
Transport in disordered media is a central theme in probability and statistical physics, where randomness in the underlying medium produces phenomena such as localization, anomalous scaling, and slow relaxation. A paradigmatic model for…