# Anne Schilling: Normal distributions of finite Markov chains

**Time: **
Mon 2020-01-27 10.30 - 11.20

**Lecturer: **
Anne Schilling, University of California, Davis

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan

### 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. This is joint work with John Rhodes based on arXiv:1902.01042 and arXiv:1711.10689 .