Renewal and memory properties in the random growth of surfaces

TL;DR

This paper investigates how cooperation in a ballistic deposition model leads to memory effects and non-Poisson renewal events in surface growth, linking these phenomena to particle velocity and diffusion processes.

Contribution

It introduces a novel connection between cooperation-induced memory and renewal properties in surface growth models, using ballistic deposition as a framework.

Findings

Cooperation induces memory effects in surface growth.

Non-Poisson renewal events are generated by the cooperative process.

Memory variable relates to particle velocity in the model.

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.