Related papers: Relaxed random walks at scale

Random Walks in Cooling Random Environments (RWCRE) is a model of random walks in dynamic random environments where the entire environment is resampled along a fixed sequence of times, called the "cooling sequence," and is kept fixed in…

We introduce a class of multifractal processes, referred to as Multifractal Random Walks (MRWs). To our knowledge, it is the first multifractal processes with continuous dilation invariance properties and stationary increments. MRWs are…

We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes…

Random diffusions are a popular tool in Monte-Carlo estimations, with well established algorithms such as Walk-on-Spheres (WoS) going back several decades. In this work, we introduce diffusion estimators for the problems of angular…

Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…

In close analogy to diffusion limited aggregation (DLA) and inspired by a work of Roux, a random walker algorithm is constructed to solve the problem of crack growth in an elastic medium. In contrast to conventional lattice approaches, the…

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…

An irreversible Markov-chain Monte Carlo (MCMC) algorithm with skew detailed balance conditions originally proposed by Turitsyn et al. is extended to general discrete systems on the basis of the Metropolis-Hastings scheme. To evaluate the…

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…

Monte Carlo random walk methods are widely used in capacitance extraction for their mesh free formulation and inherent parallelism. However, modern semiconductor technologies with densely packed structures present significant challenges in…

Multivariate Hawkes Processes (MHPs) are an important class of temporal point processes that have enabled key advances in understanding and predicting social information systems. However, due to their complex modeling of temporal…

In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…

This paper studies a non-random-walk Markov Chain Monte Carlo method, namely the Hamiltonian Monte Carlo (HMC) method in the context of Subset Simulation used for structural reliability analysis. The HMC method relies on a deterministic…

In order to tackle the problem of sampling from heavy tailed, high dimensional distributions via Markov Chain Monte Carlo (MCMC) methods, Yang, Latuszy\'nski, and Roberts (2022) (arXiv:2205.12112) introduces the stereographic projection as…

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…

We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…

In this article it is shown that the Brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete $n$-vertex ordered graph trees whose search-depth functions converge to the Brownian…

Markov chain Monte Carlo methods such as Gibbs sampling and simple forms of the Metropolis algorithm typically move about the distribution being sampled via a random walk. For the complex, high-dimensional distributions commonly encountered…

Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…

We present a graph random walk (GRW) method for the study of charge transport properties of complex molecular materials in the time-of-flight regime. The molecules forming the material are represented by the vertices of a directed weighted…