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arXiv · 2610.10860

On the Impossibility of Estimating the Average Mixing Time

Nathan A. Judd·Amedeo Roberto Esposito
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Abstract

We establish nearly-matching converse bounds on the sample complexity of estimating the average mixing time of a Markov chain from a single stationary trajectory. Unlike the worst-case mixing time, which maximises the total-variation distance to stationarity over all initial states, the average mixing time averages this distance under the stationary distribution and can therefore be substantially smaller. Our converse bounds establish when estimation is impossible, and match the key dependencies in existing achievability bounds, up to logarithmic factors. Together, these bounds provide nearly-tight PAC guarantees for estimating the average mixing time.

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Nathan A. Judd, Amedeo Roberto Esposito. 2026-10-07. On the Impossibility of Estimating the Average Mixing Time. https://arxiv.org/abs/2610.10860

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