Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site

TL;DR

This paper proves a shape theorem for a one-dimensional birth process with bounded particles per site, providing estimates on the fluctuations of the rightmost particle's position under certain assumptions.

Contribution

It establishes a shape theorem and fluctuation estimates for a one-dimensional particle system with bounded occupancy, extending understanding of such processes.

Findings

Proved a shape theorem for the system.

Derived limiting estimates for particle position.

Provided exponential bounds on fluctuations.

Abstract

We consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invariance, and non-degeneracy, we prove a shape theorem. We also derive a limiting estimate and an exponential estimate on the fluctuations of the position of the rightmost particle.