English

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