Related papers: Reinforced walks in two and three dimensions
We present a model for a random walk with memory, phenomenologically inspired in a biological system. The walker has the capacity to remember the time of the last visit to each site and the step taken from there. This memory affects the…
Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…
In this paper we consider an irreducible random walk on the integer lattice $\mathbb{Z}$ that is in the domain of normal attraction of a strictly stable process with index $\alpha\in (1, 2)$ and obtain the asymptotic form of the…
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 mixing time of a non-Markovian process, the step-reinforced random walk (SRRW) on a finite group. This process differs from a classical random walk in that at each integer time, with probability $\alpha$ the next step is chosen…
We analyze random walk in the upper half of a three dimensional lattice which goes down whenever it encounters a new vertex, a.k.a. excited random walk. We show that it is recurrent with an expected number of returns of square-root log n.
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…
In this paper, we study (1,2) and (2,1) random walks in varying environments on the lattice of positive half line. We assume that the transition probabilities at site $n$ are asymptotically constants as $n\rightarrow\infty.$ For (1,2)…
We introduce a simple technique for proving the transience of certain processes defined on the random tree $\mathcal{G}$ generated by a supercritical branching process. We prove the transience for once-reinforced random walks on…
We consider a lattice polymer model (random walk), in which the walk is allowed to visit lattice bonds at most twice. Such a model might have some relevance to describe statistical properties of RNA molecules. In order to mimic base…
The model of a tired random walker, whose jump-length decays exponentially in time, is proposed and the motion of such a tired random walker is studied systematically in one, two and three dimensional contin- uum. In all cases, the…
Quantum walks represent paradigmatic quantum evolutions, enabling powerful applications in the context of topological physics and quantum computation. They have been implemented in diverse photonic architectures, but the realization of a…
We generalize a result from Volkov [Ann. Probab. 29 (2001) 66--91] and prove that, on a large class of locally finite connected graphs of bounded degree $(G,\sim)$ and symmetric reinforcement matrices $a=(a_{i,j})_{i,j\in G}$, the…
We derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…
We consider the dynamical properties of Quantum Walks defined on the d-dimensional cubic lattice, or the homogeneous tree of coordination number 2d, with site dependent random phases, further characterised by transition probabilities…
This paper concerns a random walk that moves on the integer lattice and has zero mean and a finite variance. We obtain first an asymptotic estimate of the transition probability of the walk absorbed at the origin, and then, using the…
The study of random walks has increasingly been popular across diverse disciplines such as statistics, mathematics, quantum physics, where they are used to model paths consisting of successive random steps in a mathematical space. A…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
Polymers in confined spaces lose conformational entropy. This induces a net repulsive entropic force on the walls of the confining space. A model for this phenomenon is a lattice walk between confining walls, and in this paper a model of an…
A discrete implementation on a lattice of the Active Walker Model is presented. After the model's validity is shown in simple simulations, more complex simulations of walkers passing consecutively a lattice from an arbitrary starting point…