Binary data corruption due to a Brownian agent

TL;DR

This paper models binary data corruption caused by a Brownian agent on a lattice, providing exact calculations for corruption density and revealing extreme fluctuations through a log-normal distribution.

Contribution

It introduces a continuum model for data corruption by a Brownian agent and derives exact analytical results validated by simulations.

Findings

Exact calculation of mean corruption density

Correlation functions match simulations

Corruption density follows a log-normal distribution in 1D

Abstract

We introduce a model of binary data corruption induced by a Brownian agent (active random walker) on a d-dimensional lattice. A continuum formulation allows the exact calculation of several quantities related to the density of corrupted bits \rho; for example the mean of \rho, and the density-density correlation function. Excellent agreement is found with the results from numerical simulations. We also calculate the probability distribution of \rho in d=1, which is found to be log-normal, indicating that the system is governed by extreme fluctuations.