Related papers: Random Walks on Simplicial Complexes and Harmonics
We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index $\alpha$ ($0< \alpha \le 2$), in the symmetric case. We show that by properly scaled transition to…
We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
Despite of the extreme success of the spectral graph theory, there are relatively few papers applying spectral analysis to hypergraphs. Chung first introduced Laplacians for regular hypergraphs and showed some useful applications. Other…
We study the set of directions asymptotically explored by a spatially homogeneous random walk in $d$-dimensional Euclidean space. We survey some pertinent results of Kesten and Erickson, make some further observations, and present some…
We provide a random walk in random scenery representation of a new class of stable self-similar processes with stationary increments introduced recently by Jung, Owada and Samorodnitsky. In the functional limit theorem they provided, only a…
The Martin boundary associated with the simple random walk on an example of partially oriented lattice is shown to be trivial by computing fine estimates of the Green kernel.
Estimating characteristics of large graphs via sampling is a vital part of the study of complex networks. Current sampling methods such as (independent) random vertex and random walks are useful but have drawbacks. Random vertex sampling…
We explore some of the connections between the local picture left by the trace of simple random walk on a discrete cylinder with base a d-dimensional torus, d at least 2, of side-length N running for times of order N^{2d} and the model of…
Let $\mathcal G$ be an infinite graph -- not necessarily one-ended -- on which the simple random walk is transient. We define a variant of the continuous-time random walk on $\mathcal G$ which reaches $\infty$ in finite time and "reflects…
We consider the Activated Random Walk model in any dimension with any sleep rate and jump distribution and ergodic initial state. We show that the stabilization properties depend only on the average density of particles, regardless of how…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…
We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…
Quantum walks on undirected graphs have been studied using symmetric matrices, such as the adjacency or Laplacian matrix, and many results about perfect state transfer are known. We extend some of those results to oriented graphs. We also…
We study the operator associated to a random walk on $\R^d$ endowed with a probability measure. We give a precise description of the spectrum of the operator near $1$ and use it to estimate the total variation distance between the iterated…
We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.
In this work, we study open quantum random walks, as described by S. Attal et al. These objects are given in terms of completely positive maps acting on trace-class operators, leading to one of the simplest open quantum versions of the…
We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…