Combinatorial considerations on the invariant measure of a stochastic matrix

2019/10/07 by Artur Stephan, Stephan, Artur
Computer Science · Engineering · Mathematics · #60Jxx #FOS: Mathematics #Matrix Theory and Algorithms #Probability (math.PR) #advanced mathematical theories #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1910.02856

openalex publication_date 2019/10/07 · openalex created_date 2019/10/10 · openalex updated_date 2026/07/28

Abstract

The invariant measure is a fundamental object in the theory of Markov processes. In finite dimensions a Markov process is defined by transition rates of the corresponding stochastic matrix. The Markov tree theorem provides an explicit representation of the invariant measure of a stochastic matrix. In this note, we given a simple and purely combinatorial proof of the Markov tree theorem. In the symmetric case of detailed balance, the statement and the proof simplifies even more.

Citations

• Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird

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