相关论文: New insights on the reinforced Elephant Random Wal…

A $\delta$ once-reinforced random walk ($\delta$-ORRW) on connected graph is a self-interacting random walk which moves to its neighbors at each step according to the weights of the edges at that time, where the weights are $1$ on edges…

Vertex-reinforced random walk (VRRW), defined by Pemantle in 1988, is a random process that takes values in the vertex set of a graph G, which is more likely to visit vertices it has visited before. Pemantle and Volkov considered the case…

Elephant random walk is a kind of one-dimensional discrete-time random walk with infinite memory: For each step, with probability $\alpha$ the walker adopts one of his/her previous steps uniformly chosen at random, and otherwise he/she…

We show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional CTRW. This asymptotic equivalence is effected by a…

Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…

We review various features of the statistics of random paths on graphs. The relationship between path statistics and Quantum Mechanics (QM) leads to two canonical ways of defining random walk on a graph, which have different statistics and…

In this report, we introduce the elephant random walk on the triangular lattice over $R^2$ incorporating directions by extending the model developed in \cite{baur2016elephant}. We study the behavior of the walk by finding the appropriate…

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic…

For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…

Using the continuous-time random walk (CTRW) approach, we study the phenomenon of relaxation of two-state systems whose elements evolve according to a dichotomous process. Two characteristics of relaxation, the probability density function…

We give a short proof of the recurrence of the two-dimensional elephant random walk in the diffusive regime. This was recently established by Shuo Qin, but our proof only uses very rough comparison with the standard plane random walk. We…

We study once-reinforced random walk (ORRW) on $\mathbb Z$. For this model, we derive limit results on all moments of its range using Tauberian theory.

A survey of reinforced random walk, with emphasis on the linear case.

Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard…

This article studies vertex reinforced random walks that are non-backtracking (denoted VRNBW), i.e. U-turns forbidden. With this last property and for a strong reinforcement, the emergence of a path may occur with positive probability.…

Very often when studying non-equilibrium systems one is interested in analysing dynamical behaviour that occurs with very low probability, so called rare events. In practice, since rare events are by definition atypical, they are often…

We consider in this article an Elephant Random Walk evolving in the plane. Specifically, this is a reinforced stochastic process in which the $n$th step is given by a random rotation of one of the previous steps chosen uniformly at random.…

This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…

We give a complete and unified description -- under some stability assumptions -- of the functional scaling limits associated with some persistent random walks for which the recurrent or transient type is studied in [1]. As a result, we…

This work introduces the notion of edge oriented reinforced random walk which proposes in a general framework an alternative understanding of the annealed law of random walks in random environment.