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There is a long history of establishing central limit theorems for Markovchains. Quantitative bounds for chains with a spectral gap were proved by Mannand refined later. Recently, rates of convergence for the total variationdistance were obtained for random walks on expander graphs, which are oftenused to generate sequences satisfying desirable pseudorandom properties. Weprove a local central limit theorem with an explicit rate of convergence forrandom walks on expander graphs, and derive an improved bound for the totalvariation distance.

A local central limit theorem for random walks on expander graphs