English

Analytic-geometric methods for finite Markov chains with applications to quasi-stationarity

Probability 2019-06-13 v1

Abstract

For a relatively large class of well-behaved absorbing (or killed) finite Markov chains, we give detailed quantitative estimates regarding the behavior of the chain before it is absorbed (or killed). Typical examples are random walks on box-like finite subsets of the square lattice Zd\mathbb Z^d absorbed (or killed) at the boundary. The analysis is based on Poincar\'e, Nash, and Harnack inequalities, moderate growth, and on the notions of John and inner-uniform domains.

Keywords

Cite

@article{arxiv.1906.04877,
  title  = {Analytic-geometric methods for finite Markov chains with applications to quasi-stationarity},
  author = {Persi Diaconis and Kelsey Houston-Edwards and Laurent Saloff-Coste},
  journal= {arXiv preprint arXiv:1906.04877},
  year   = {2019}
}