English

Normal distributions of finite Markov chains

Probability 2020-03-09 v1 Combinatorics Group Theory

Abstract

We show that the stationary distribution of a finite Markov chain can be expressed as the sum of certain normal distributions. These normal distributions are associated to planar graphs consisting of a straight line with attached loops. The loops touch only at one vertex either of the straight line or of another attached loop. Our analysis is based on our previous work, which derives the stationary distribution of a finite Markov chain using semaphore codes on the Karnofsky--Rhodes and McCammond expansion of the right Cayley graph of the finite semigroup underlying the Markov chain.

Keywords

Cite

@article{arxiv.1902.01042,
  title  = {Normal distributions of finite Markov chains},
  author = {John Rhodes and Anne Schilling},
  journal= {arXiv preprint arXiv:1902.01042},
  year   = {2020}
}

Comments

14 pages. arXiv admin note: text overlap with arXiv:1711.10689

R2 v1 2026-06-23T07:31:04.392Z