Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site
Probability
2022-02-23 v2
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.
Keywords
Cite
@article{arxiv.1911.12867,
title = {Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site},
author = {Viktor Bezborodov and Luca Di Persio and Tyll Krueger},
journal= {arXiv preprint arXiv:1911.12867},
year = {2022}
}
Comments
17 pages; a short section devoted to numerical simulations is added; other small changes and improvements