Related papers: Excited Random Walk in One Dimension

We study a random walk in a N dimensional hypercube and exhibit results about stopping times when N diverges. The first theorem discusses the time in which two coupling processes spend to meet. A corollary provides a majorant for the…

We study a strongly Non-Markovian variant of random walk in which the probability of visiting a given site $i$ is a function $f$ of number of previous visits $v(i)$ to the site. If the probability is proportional to number of visits to the…

The recurrence properties of random walks can be characterized by P\'{o}lya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random…

Analytical results for the distribution of first hitting times of random walks on Erd\H{o}s-R\'enyi networks are presented. Starting from a random initial node, a random walker hops between adjacent nodes until it hits a node which it has…

In this paper, we study the discrete-time quantum random walks on a line subject to decoherence. The convergence of the rescaled position probability distribution $p(x,t)$ depends mainly on the spectrum of the superoperator…

In this paper we consider a particular version of the random walk with restarts: random reset events which bring suddenly the system to the starting value. We analyze its relevant statistical properties like the transition probability and…

This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The…

We study the favourite sites of a random walk evolving in a sparse random environment on the set of integers. The walker moves symmetrically apart from some randomly chosen sites where we impose random drift. We prove annealed limit…

We develop rigorous, analytic techniques to study the behaviour of biased random walks on combs. This enables us to calculate exactly the spectral dimension of random comb ensembles for any bias scenario in the teeth or spine. Two specific…

We study the escape probability problem in random walks over graphs. Given vertices, $s,t,$ and $p$, the problem asks for the probability that a random walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be…

We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter $\kappa>0$ that determines the fluctuations of the process.…

As an extension of Polya's classical result on random walks on the square grids ($\Z^d$), we consider a random walk where the steps, while still have unit length, point to different directions. We show that in dimensions at least 4, the…

We study a discrete time self interacting random process on graphs, which we call Greedy Random Walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not…

Several phase transitions for excited random walks on the integers are known to be characterized by a certain drift parameter delta. For recurrence/transience the critical threshold is |delta|=1, for ballisticity it is |delta|=2 and for…

We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the waiting…

We analyze the differences between the horizontal and the vertical component of the simple random walk on the 2-dimensional comb. In particular we evaluate by combinatorial methods the asymptotic behaviour of the expected value of the…

We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…

Let $N$ and $M$ be positive integers satisfying $1\le M\le N$, and let $0<p_0<p_1<1$. Define a process $\{X_n\}_{n=0}^\infty$ on $\mathbb{Z}$ as follows. At each step, the process jumps either one step to the right or one step to the left,…

We consider random walks on the line given by a sequence of independent identically distributed jumps belonging to the strict domain of attraction of a stable distribution, and first determine the almost sure exponential divergence rate, as…

We consider the limit behavior of an excited random walk (ERW), i.e., a random walk whose transition probabilities depend on the number of times the walk has visited to the current state. We prove that an ERW being naturally scaled…