Renewal and memory properties in the random growth of surfaces

Abstract

We use the model of ballistic deposition as a simple way to establish cooperation among the columns of a growing surface, \emph{the single individual of the same society}. We show that cooperation generates memory properties and at same time non-Poisson renewal events. The variable generating memory can be regarded as the velocity of a particle driven by a bath with the same time scale, and the variable generating renewal processes is the corresponding diffusional coordinate.