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Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
Random walks on dynamic graphs have received increasingly more attention from different academic communities over the last decade. Despite the relatively large literature, little is known about random walks that construct the graph where…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local…
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…
We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its…
We discuss various models for epidemics on networks that rely on Markov chains. Random walks on graphs are often used to predict epidemic spread and to investigate possible control actions to mitigate them. In this study, we demonstrate…
The branching annihilating random walk is studied on a random graph whose sites have uniform number of neighbors (z). The Monte Carlo simulations in agreement with the generalized mean-field analysis indicate that the concentration decreses…
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…
Numerical and theoretical studies of a one-dimensional spin model with locally broken spin symmetry are presented. The multi-species annihilating random walk transition found at zero branching rate previously is investigated now concerning…
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…
We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability…
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…
The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…
Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…
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 consider a continuous-time branching random walk on $\mathbb{Z}$ in a random non homogeneous environment. Particles can walk on the lattice points or disappear with random intensities. The process starts with one particle at initial time…
We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a…