A class of non-reversible hypercube long-range random walks and Bernoulli autoregression

TL;DR

This paper introduces a broad class of non-reversible long-range random walks on hypercubes, linking them to multivariate Bernoulli autoregression, and explores their properties and applications.

Contribution

It presents a novel class of non-reversible hypercube random walks and establishes their connection with multivariate Bernoulli autoregression.

Findings

Characterization of non-reversible hypercube random walks

Connection established with multivariate Bernoulli autoregression

Potential applications in high-dimensional stochastic processes

Abstract

We study a large class of long-range random walks which take values on the vertices of an N dimensional hypercube. These processes are connected with multivariate Bernoulli autoregression.