相关论文: Activated Random Walks

Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…

Application of CTRW to dipole hopping transport is considered. Correct versions of derivation of the CTRW-equations are presented. Existence of different forms of memory kernels is demonstrated. Correction of Scher-Lax memory kernel within…

We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…

Proceedings of the 1st International Workshop on Robot Learning and Planning (RLP 2016)

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…

Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random Environment (RWRE) on $\Bbb{Z}^d$ where the transition probabilities are i.i.d. at each site with a Dirichlet distribution. Hence, the model is parametrized…

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random…

Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief…

We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…

We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…

Background: This study is mainly motivated by the need of understanding how the diffusion behaviour of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell,…

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

The present overview of interacting particle systems on random graphs collects the notes of a mini-course given by the authors at the Brazilian School of Probability, 5--9 August 2024, in Salvador, Bahia, Brazil. The content is a personal…

We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning…

We consider Activated Random Walks on arbitrary finite networks, with particles being inserted at random and absorbed at the boundary. Despite the non-reversibility of the dynamics and the lack of knowledge on the stationary distribution,…

Learning a diverse set of skills by interacting with an environment without any external supervision is an important challenge. In particular, obtaining a goal-conditioned agent that can reach any given state is useful in many applications.…

We consider a variant of random walks on finite groups. At each step, we choose an element from a set of generators ("directions") uniformly, and an integer from a power law ("speed") distribution associated with the chosen direction. We…

We investigate a connection between a property of the distribution and a conserved quantity for the reversible cellular automaton derived from a discrete-time quantum walk in one dimension. As a corollary, we give a detailed information of…

Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the…

In this note, we give an original convergence result for products of independent random elements of motion group. Then we consider dynamic random walks which are inhomogeneous Markov chains whose transition probability of each step is, in…