相关论文: Returns to origin of a one-dimensional random walk…

We study the limit behaviour of a class of random walk models taking values in the $d$-dimensional unit standard simplex, $d\ge 1$, defined as follows. From an interior point $z$, the process chooses one of the $d+1$ vertices of the…

We consider a random walk on integers where at the first visits to a site the walker gets a positive drift, but where after a certain number of visits the walker gets a negative drift. We prove that the walker is almost surely transient to…

In this paper, we propose and analyze a novel one-dimensional inhomogeneous random walk model that combines spatial decay of transition probabilities with a temporal renewal structure for each excursion. In this model, the probability of…

We consider a self-attracting random walk in dimension d=1, in presence of a field of strength s, which biases the walker toward a target site. We focus on the dynamic case (true reinforced random walk), where memory effects are implemented…

We study the asymptotic behaviour of the number of times the elephant random walk in the critical regime visits the origin. Our result entails that most zeros of the critical elephant random walk occur shortly before its last passage time…

Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…

A new proof is given for the formula for the expected return time of a random walk on a graph. This proof makes use of known relationships between electric resistance and random walks.

In this short paper, we consider the Once-reinforced random walk with reinforcement parameter $a$ on trees with bounded degree which are transient for the simple random walk. On each of these trees, we prove that there exists an explicit…

The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional…

We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance…

We define a random walk problem which admits analytic results, on a class of infinite periodic lattices which are directed and colored. Our approach is motivated from the fact that such lattices arise in string theoretic constructs of…

This is the third in a series of papers in which we consider one-dimensional Random Walk in Cooling Random Environment (RWCRE). The latter is obtained by starting from one-dimensional Random Walk in Random Environment (RWRE) and resampling…

This paper considers the question: how many times does a simple random walk revisit the most frequently visited site among the inner boundary points? It is known that in ${\mathbb{Z}}^2$, the number of visits to the most frequently visited…

For normally reflected Brownian motion and for simple random walk on independently growing in time d-dimensional domains, d>=3, we establish a sharp criterion for recurrence versus transience in terms of the growth rate.

We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…

We study a self-attractive random walk such that each trajectory of length $N$ is penalised by a factor proportional to $\exp ( - |R_N|)$, where $R_N$ is the set of sites visited by the walk. We show that the range of such a walk is close…

An overview is presented of recent work on some statistical problems on multiparticle random walks. We consider a Euclidean, deterministic fractal or disordered lattice and N >> 1 independent random walkers initially (t=0) placed onto the…

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…

In this paper we consider a d-dimensional scenery seen along a simple symmetric branching random walk, where at each time each particle gives the color record it is seeing. We show that we can a.s. reconstruct the scenery up to equivalence…

We consider random walks X_n in Z+, obeying a detailed balance condition, with a weak drift towards the origin when X_n tends to infinity. We reconsider the equivalence in law between a random walk bridge and a 1+1 dimensional…