Binary data corruption due to a Brownian agent

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.