Toy examples for effective concentration bounds

2021/02/18 by Kloeckner, Benoît
#Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2102.09215

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).

Related

• Effective limit theorems for Markov chains with a spectral gap
• Concentration inequalities for Markov chains by Marton couplings and spectral methods
• Concentration of Markov chains with bounded moments
• Two Examples of COM Bounds using Spectral Gaps: Length of the LIS in a\n Random Permutation and Lipschitz Functions of 1d Markov Chains
• Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-type inequalities for Markov chains and related processes