Related papers: Walkers on the circle
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…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform avoidance coupling. We show that the only Markovian avoidance coupling on a cycle is of…
Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. This paper marks the initial stride toward achieving this…
We observe body-rotation behavior of pedestrians to avoid others when they are moving in congested situations. In such cases, body orientation often differs from walking direction, i.e., pedestrians step sideways. In this paper, we focused…
In this paper we consider the one-dimensional, biased, randomly trapped random walk when the trapping times have infinite variance. We prove sufficient conditions for the suitably scaled walk to converge to a transformation of a stable…
In [1], the authors consider a random walk $(Z_{n,1},\ldots,Z_{n,K+1})\in \mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. A functional central limit theorem for the first…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
A survey is presented of known results concerning simple random walk on the class of distance-regular graphs. One of the highlights is that electric resistance and hitting times between points can be explicitly calculated and given strong…
We identify a relationship between a certain family of random walks on Euclidean lattices and difference matrices over cyclic groups. We then use the techniques of Fourier analysis to estimate the return probabilities of these random walks,…
We investigate the eigenvalue statistics of random Bernoulli matrices, where the matrix elements are chosen independently from a binary set with equal probability. This is achieved by initiating a discrete random walk process over the space…
The possibility to understand and to quantitatively model the physics of the interactions between pedestrians walking in crowds has compelling relevant applications, e.g. related to the design and safety of civil infrastructures. In this…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
Understanding how simple local interactions give rise to emergent exploration patterns is a fundamental question in statistical physics. We introduce a minimal model of two coupled agents that avoid retracing their own paths while being…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
Motivated by a problem arising from pharmaceutical science [B. Baeumer et al., Discr. Contin. Dyn. Sys. B 12], we study random walks on the contact graph of a bidisperse random sphere packing. For a random walk on the unweighted graph that…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time…
Random walks on discrete lattices are fundamental models that form the basis for our understanding of transport and diffusion processes. For a single random walker on complex networks, many properties such as the mean first passage time and…