Zeon Algebra, Fock Space, and Markov Chains

TL;DR

This paper introduces Fock spaces over zeons, develops trace identities and a noncommutative integration-by-parts formula, and applies these to establish a new ergodicity criterion for Markov chains that does not rely on transition matrix powers.

Contribution

It presents the novel concept of Fock spaces over zeons and derives new mathematical tools and criteria for analyzing Markov chain ergodicity.

Findings

Established trace identities for zeon Fock spaces

Developed a noncommutative integration-by-parts formula

Derived a new ergodicity criterion for Markov chains

Abstract

Fock spaces over zeons are introduced. Trace identities and a noncommutative "integration-by-parts" formula are developed. As an application, we find a new criterion, without involving powers of the transition matrix, for a Markov chain to be ergodic.