Related papers: Random Walk in Random Environment: A short introdu…
Graphs are often used to organize data because of their simple topological structure, and therefore play a key role in machine learning. And it turns out that the low-dimensional embedded representation obtained by graph representation…
We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…
Random walks in cones have the double interest of being at the heart of many probabilistic problems and of being related to many mathematical fields, such as spectral theory, combinatorics, or discrete complex analysis. In this article, we…
We study survival of nearest-neighbour branching random walks in random environment (BRWRE) on ${\mathbb Z}$. A priori there are three different regimes of survival: global survival, local survival, and strong local survival. We show that…
A well known connection between first-passage probability of random walk and distribution of electrical potential described by Laplace equation is studied. We simulate random walk in the plane numerically as a discrete time process with…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning…
Random walk sampling methods have been widely used in graph sampling in recent years, while it has bias towards higher degree nodes in the sample. To overcome this deficiency, classical methods such as MHRW design weighted walking by…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
The purpose of this short note is to establish a connection between a one-dimensional random walk in a random sparse environment and the random pinning model. We show that the grand canonical partition function of the pinning model…
We study a simple random walk on Z^2 with constraints on the axis. Motivation comes from physics when particles (a gas for example, see [Dal88]) are submitted to a local field. In our case we assume that the particle evolves freely in the…
The paper consists of two parts. In the first part we review recent work on limit theorems for random walks in random environment (RWRE) on a strip with jumps to the nearest layers. In the second part, we prove the quenched Local Limit…
We consider a system of independent random walks in a common random environment. Previously, a hydrodynamic limit for the system of RWRE was proved under the assumption that the random walks were transient with positive speed. In this paper…
A notion of random walks for circle packings is introduced. The geometry behind this notion is discussed, together with some applications. In particular, we obtain a short proof of a result regarding the type problem for circle packings,…
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…
Reinforced random walks (RRWs), including vertex-reinforced random walks (VRRWs) and edge-reinforced random walks (ERRWs), model random walks where the transition probabilities evolve based on prior visitation history~\cite{mgr, fmk,…
Random walk is an explainable approach for modeling natural processes at the molecular level. The Random Permutation Set Theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer Theory.…
We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…
Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical…
Motivation: Over the past decade, network-based approaches have proven useful in identifying disease modules within the human interactome, often providing insights into key mechanisms and guiding the quest for therapeutic targets. This is…