Related papers: Conservative and semiconservative random walks: re…
In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
We study the path behavior of the symmetric walk on some special comb-type subsets of ${\mathbb Z}^2$ which are obtained from ${\mathbb Z}^2$ by generalizing the comb having finitely many horizontal lines instead of one.
We study linear random walks on the torus and show a quantitative equidistribution statement, under the assumption that the Zariski closure of the acting group is semisimple.
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…
In this paper, we show that "Labyrinth walks", the conservative version of "Labyrinth chaos" and member of the Thomas-R\"ossler class of systems, does not admit an autonomous Hamiltonian as a constant function in time, and as a consequence,…
In part I (math.PR/0406392) we proved for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n is of the maximal order square root of n. In higher dimensions we call…
In the present paper, as a continuation of our preceding paper [10], we study another kind of central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering graphs from a viewpoint of discrete geometric analysis…
Consider a one dimensional simple random walk $X=(X_n)_{n\geq0}$. We form a new simple symmetric random walk $Y=(Y_n)_{n\geq0}$ by taking sums of products of the increments of $X$ and study the two-dimensional walk…
In this paper, we construct families of polynomials defined by recurrence relations related to mean-zero random walks. We show these families of polynomials can be used to approximate $z^n$ by a polynomial of degree $\sim \sqrt{n}$ in…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…
Consider an arbitrary transient random walk on $\Z^d$ with $d\in\N$. Pick $\alpha\in[0,\infty)$ and let $L_n(\alpha)$ be the spatial sum of the $\alpha$-th power of the $n$-step local times of the walk. Hence, $L_n(0)$ is the range,…
For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the…
We analyze random walks on a class of semigroups called ``left-regular bands''. These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are…
The range process $R_n$ of a random walk is the collection of sites visited by the random walk up to time $n$. In this work we deal with the question of whether the range process of a random walk or the range process of a cocycle over an…
We introduce and study a family of random processes on trees we call hipster random walks, special instances of which we heuristically connect to the min-plus binary trees introduced by Robin Pemantle and studied by Auffinger and Cable…
The subject of this paper is the simple random walk on $\mathbb{Z}$. We give a very simple answer to the following problem: under the condition that a random walk has already spent $\alpha$-percent of the traveling time on the positive side…
We give an equivalent characterisation for the existence of a semi-conjugacy to an irrational rotation for conservative homeomorphisms of the two-torus. This leads to an analogue of Poincare's classification of circle homeomorphisms for…
In this article subordination of random walks in $R^d$ is considered. We prove that subordination of random walks in the sense of [BSC12] yields the same process as subordination of L\'evy processes (in the sense of Bochner). Furthermore,…