Related papers: The strong interaction limit of continuous-time we…
We derive a functional central limit theorem for the excursion of a random walk conditioned on sweeping a prescribed geometric area. We assume that the increments of the random walk are integer-valued, centered, with a third moment equal to…
Lock step walker model is a one-dimensional integer lattice walker model in discrete time. Suppose that initially there are infinitely many walkers on the non-negative even integer sites. At each tick of time, each walker moves either to…
We present simulations of self-avoiding random walks on 2-d lattices with the topology of an infinitely long cylinder, in the limit where the cylinder circumference L is much smaller than the Flory radius. We study in particular the…
This paper studies a recently proposed continuous-time distributed self-appraisal model with time-varying interactions among a network of $n$ individuals which are characterized by a sequence of time-varying relative interaction matrices.…
Given a random walk $(S_n)$ with typical step distributed according to some fixed law and a fixed parameter $p \in (0,1)$, the associated positively step-reinforced random walk is a discrete-time process which performs at each step, with…
We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
The probability distributions of discrete-time quantum walks have been often investigated, and many interesting properties of them have been discovered. The probability that the walker can be find at a position is defined by diagonal…
The double dimer model is defined as the superposition of two independent uniformly distributed dimer covers of a graph. Its configurations can be viewed as disjoint collections of self-avoiding loops. Our first result is that in…
We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of walker's…
We study the quenched behaviour of a perturbed version of the simple symmetric random walk on the set of integers. The random walker moves symmetrically with an exception of some randomly chosen sites where we impose a random drift. We show…
By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we investigate the coupled effects of random walk and intragroup interaction on contagion. Compared with the…
A step-reinforced random walk is a discrete-time stochastic process with long-range dependence. At each step, with a fixed probability $\alpha$, the so-called positively step-reinforced random walk repeats one of its previous steps, chosen…
We study the distribution of dynamical quantities in various one-dimensional, disordered models the critical behavior of which is described by an infinite randomness fixed point. In the {\it disordered contact process}, the quenched…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
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…
Building on a work by Alm, we consider a model of weighted self-avoiding walks on a lattice and develop a method for computing upper bounds on the corresponding weighted connective constant, which we implement in a publicly available…
This article is dedicated to the study of the 2-dimensional interacting prudent self-avoiding walk (referred to by the acronym IPSAW) and in particular to its collapse transition. The interaction intensity is denoted by $\beta>0$ and the…