Random walk with multiple memory channels: a new paradigm

2025/06/18 by Saha, Surajit · 2 citations
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2506.15145

Abstract

A new class of one-dimensional, discrete time random walk model with memory, termed "Random walk with n memory channels" (RWnMC) is proposed. In this model the information of n (n∈ ℤ) previous steps from the walker's entire history are needed to decide future step. Exact calculation of the mean and variance of position of the RW2MC (n=2) has been done which shows that it can lead to asymptotic diffusive and superdiffusive behavior in different parameter regimes. A connection between RWnMC and Pólya type urn model evolving by n drawings has also been reported. This connection for the RW2MC is discussed in detail which suggests the applicability of RW2MC in many population dynamics model with multiple competing species.

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