AI & ML
On the Impossibility of Estimating the Average Mixing Time
arXiv math.IT0 views
arXiv:2610.10860v1 Announce Type: cross 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.
Source：https://arxiv.org/abs/2610.10860PreviousHow Many Repeated Pairwise Comparisons Are Needed for Ranking under Heterogeneity?NextLow-complexity Equalization of Zak-OTFS Via Neumann Series
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