Related papers: Non-Backtracking Centrality Based Random Walk on N…

We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…

We study the so-called elephant random walk (ERW) which is a non-Markovian discrete-time random walk on $\mathbb{Z}$ with unbounded memory which exhibits a phase transition from diffusive to superdiffusive behaviour. We prove a law of large…

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…

Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random…

Due to wide applications in diverse fields, random walks subject to stochastic resetting have attracted considerable attention in the last decade. In this paper, we study discrete-time random walks on complex network with multiple resetting…

We present analytical results for the distribution of first hitting times of random walks (RWs) on random regular graphs (RRGs) of degree $c \ge 3$ and a finite size $N$. Starting from a random initial node at time $t=1$, at each time step…

Network embedding, which maps graphs to distributed representations, is a unified framework for various graph inference tasks. According to the topology properties (e.g., structural roles and community memberships of nodes) to be preserved,…

Let X be a locally finite, connected graph without vertices of degree 1. Non-backtracking random walk moves at each step with equal probability to one of the "forward" neighbours of the actual state, i.e., it does not go back along the…

This paper proposes an attributed network growth model. Despite the knowledge that individuals use limited resources to form connections to similar others, we lack an understanding of how local and resource-constrained mechanisms explain…

This thesis explores a central question: how does memory affect the way random walkers explore space? By analyzing various non-Markovian models, where past behavior directly influences future dynamics, we uncover new mechanisms and…

Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…

It is well known that the weak limit of a suitably scaled continuous-time random walk (CTRW) is the Brownian motion. We investigate the convergence of certain patterned random matrices whose entries are independent CTRWs and their…

Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states, for example those employed in…

We provide analytical solutions for two types of random walk: generic random walk (GRW) and maximal entropy random walk (MERW) on a Cayley tree with arbitrary branching number, root degree, and number of generations. For MERW, we obtain the…

A random walk on a $N$-dimensional hypercube is a discrete time stochastic process whose state space is the set $\{-1,+1\}^{N}$, which has uniform probability of reaching any neighbour state, and probability zero of reaching a non-neighbour…

Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…

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…

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…

Relaxed random walk (RRW) models of trait evolution introduce branch-specific rate multipliers to modulate the variance of a standard Brownian diffusion process along a phylogeny and more accurately model overdispersed biological data.…

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…