Related papers: Reinforced random walk
This paper extends the result of Broniatowski and Caron (2013) pertaining to the asymptotic distribution of a random walk conditioned on its final value as the number of summands increase. We consider multivariate light-tailed random walk…
In this paper we introduce the notion of Random Walk in Changing Environment - a random walk in which each step is performed in a different graph on the same set of vertices, or more generally, a weighted random walk on the same vertex and…
In operator algebra, the linearization trick is a technique that reduces the study of a non-commutative polynomial evaluated at elements of an algebra A to the study of a polynomial of degree one, evaluated on the enlarged algebra A x M r…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
Excited random walk is a process that has a drift to the right whenever it encounters a new vertex. The paper shows that in two dimensions it drifts to the right linearly in time.
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
We consider a weighted random walk on the backbone of an oriented percolation cluster. We determine necessary conditions on the weights for Brownian scaling limits under the annealed and the quenched law. This model is a random walk in…
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…
Reinforced Galton--Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forebears can be repeated randomly by descendants. More specifically, the evolution…
The authors propose a new variation of random walks called ladder chains $L(r,s,p)$. We extend concepts such as ruin probability, hitting time, transience and recurrence of random walks to ladder chain. Take $L(2,2,p)$ for instance, we find…
We consider several variants of a class of random walks whose increment distributions depend on the average value of the process over its most recent $N$ steps. We investigate the speed of the process, and in particular, the limiting speed…
In a recent paper [2] the author introduced and investigated a random walk model similar to a model introduced in [1]. In these models the increment of the random walk depends on the complete past of the process. In this note I will point…
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…
Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
In the information overloaded web, personalized recommender systems are essential tools to help users find most relevant information. The most heavily-used recommendation frameworks assume user interactions that are characterized by a…
We consider a random walk $\tilde S$ which has different increment distributions in positive and negative half-planes. In the upper half-plane the increments are mean-zero i.i.d. with finite variance. In the lower half-plane we consider two…
We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On $\Z^d$, RWDE are parameterized…
The paper is concerned with a new approach for the recurrence property of the oscillating process on $\mathbb{Z}$ in Kemperman's sense. In the case when the random walk is ascending on $\mathbb{Z}^-$ and descending on $\mathbb{Z}^+$, we…