相关论文: Variations of the elephant random walk
The following random process on $\Z^4$ is studied. At first visit to a site, the two first coordinates perform a (2-dimensional) simple random walk step. At further visits, it is the last two coordinates which perform a simple random walk…
Random walks (RWs) are fundamental stochastic processes with applications across physics, computer science, and information processing. A recent extension, the laser chaos decision-maker, employs chaotic time series from semiconductor…
Random walk is an explainable approach for modeling natural processes at the molecular level. The Random Permutation Set Theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer Theory.…
We prove a quenched invariance principle for a class of random walks in random environment on $\mathbb{Z}^d$, where the walker alters its own environment. The environment consists of an outgoing edge from each vertex. The walker updates the…
This paper is devoted to the asymptotic analysis of the amnesic elephant random walk (AERW) using a martingale approach. More precisely, our analysis relies on asymptotic results for multidimensional martingales with matrix normalization.…
A family of walks confined to the first orthant whose defining stepset has drift outside of the region can be challenging to sample uniformly at random for large lengths. We address this by generalizing the 2D walk sampler of Lumbroso et…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
We consider a random walk with transition probabilities weakly dependent on an environment with a deterministic, but strongly chaotic, evolution. We prove that for almost all initial conditions of the environment the walk satisfies the CLT.
In a step reinforced random walk, at each integer time and with a fixed probability p $\in$ (0, 1), the walker repeats one of his previous steps chosen uniformly at random, and with complementary probability 1 -- p, the walker makes an…
Self-interacting random walks are endowed with long range memory effects that emerge from the interaction of the random walker at time $t$ with the territory that it has visited at earlier times $t'<t$. This class of non Markovian random…
In this paper we study some properties of random walks perturbed at extrema, which are generalizations of the walks considered e.g., in Davis (1999). This process can also be viewed as a version of {\em excited random walk}, studied…
A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial…
Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general…
We derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…
The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same…
We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random walk…
In this work, we discuss the smoothly amnesia-reinforced multidimensional elephant random walk (MARW). The scaling limit of the MARW is shown to exist in the diffusive, critical and superdiffusive regimes. We also establish the almost sure…
The random walk in Dirichlet environment is a random walk in random environment where the transition probabilities are independent Dirichlet random variables. This random walk exhibits a property of statistical invariance by time-reversal…
A rotor configuration on a graph contains in every vertex an infinite ordered sequence of rotors, each is pointing to a neighbor of the vertex. After sampling a configuration according to some probability measure, a rotor walk is a…