English

Cookie branching random walks

Probability 2013-04-19 v2

Abstract

We consider a branching random walk on Z\Z, where the particles behave differently in visited and unvisited sites. Informally, each site on the positive half-line contains initially a cookie. On the first visit of a site its cookie is removed and particles at positions with a cookie reproduce and move differently from particles on sites without cookies. Therefore, the movement and the reproduction of the particles depend on the previous behaviour of the population of particles. We study the question if the process is recurrent or transient, i.e., whether infinitely many particles visit the origin or not.

Cite

@article{arxiv.1106.1688,
  title  = {Cookie branching random walks},
  author = {Christian Bartsch and Michael Kochler and Thomas Kochler and Sebastian Müller and Serguei Popov},
  journal= {arXiv preprint arXiv:1106.1688},
  year   = {2013}
}

Comments

2 figures Revised version, to appear in ALEA, differs slightly from the published version due to typesetting

R2 v1 2026-06-21T18:19:43.193Z