Toy examples for effective concentration bounds

TL;DR

This paper establishes explicit spectral gap estimates for various Markov chains, enabling the application of concentration inequalities and advancing the understanding of their convergence properties.

Contribution

It provides explicit spectral gap bounds for different Markov chains, which are rarely available, facilitating more precise concentration results.

Findings

Spectral gaps are proven for multiple Markov chains.

Explicit estimates enable effective concentration bounds.

Results improve understanding of Markov chain convergence.

Abstract

In this note we prove a spectral gap for various Markov chains on various functional spaces. While proving that a spectral gap exists is relatively common, explicit estimates seems somewhat rare.These estimates are then used to apply the concentration inequalities of "Effective limit theorems for Markov chains with a spectral gap" (most of the present material was part of Section 3 of that article, which has been reduced to its core in the published version).