Related papers: Localization of reinforced random walks
We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on a $d$-dimensional lattice containing one trapping site. Due to reinforcement, a phase transition occurs when the…
We establish annealed and quenched invariance principles for random walks in random conductances lifted to the p-variation rough path topology, allowing for degenerate environments and long-range jumps. Our proof is based on a unified…
We study a distinguished random walk on affine buildings of type Ar , which was already considered by Cartwright, Saloff-Coste and Woess. In rank r=2, it is the simple random walk and we obtain optimal global bounds for its transition…
We consider quantum walks defined on arbitrary infinite graphs, parameterized by a family of scattering matrices attached to the vertices. Multiplying each scattering matrix by an i.i.d. random phase, we obtain a random scattering quantum…
Random walks on expanders play a crucial role in Markov Chain Monte Carlo algorithms, derandomization, graph theory, and distributed computing. A desirable property is that they are rapidly mixing, which is equivalent to having a spectral…
Random walks on dynamic graphs have received increasingly more attention from different academic communities over the last decade. Despite the relatively large literature, little is known about random walks that construct the graph where…
We consider a random walk in a random environment (RWRE) on the strip of finite width $\mathbb{Z} \times \{1,2,\ldots,d\}$. We prove both quenched and averaged large deviation principles for the position and the hitting times of the RWRE.…
We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the…
Sood and Grassberger studied in [Phys. Rev. Lett. 99, 098701 (2007)] random walks on random graphs that are biased towards a fixed target point. They put forward a critical bias strength b_c such that a random walker on an infinite graph…
We investigate the asymptotic behaviour of a class of self-interacting nearest neighbour random walks on the one-dimensional integer lattice which are pushed by a particular linear combination of their own local time on edges in the…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
Consider the setting of multiple random walks (RWs) on a graph executing a certain computational task. For instance, in decentralized learning via RWs, a model is updated at each iteration based on the local data of the visited node and…
Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity…
We consider controlled random walks that are martingales with uniformly bounded increments and nontrivial jump probabilities and show that such walks can be constructed so that P(S_n^u=0) decays at polynomial rate n^{-\alpha} where \alpha>0…
We consider a random walk on $\R^d$ in a polynomially mixing random environment that is refreshed at each time step. We use a martingale approach to give a necessary and sufficient condition for the almost-sure functional central limit…
We introduce a new type of random walk where the definition of edge reinforcement is very different from the one in the reinforced random walk models studied so far, and investigate its basic properties, such as null/positive recurrence,…
The aim of this paper is the study of the strong local survival property for discrete-time and continuous-time branching random walks. We study this property by means of an infinite dimensional generating function G and a maximum principle…
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…
Random walks are a fundamental primitive used in many machine learning algorithms with several applications in clustering and semi-supervised learning. Despite their relevance, the first efficient parallel algorithm to compute random walks…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…