# A characterization of $L_{2}$ mixing and hypercontractivity via hitting times and maximal inequalities

@inproceedings{Hermon2016ACO, title={A characterization of \$L_\{2\}\$ mixing and hypercontractivity via hitting times and maximal inequalities}, author={Jonathan Hermon and Yuval Peres}, year={2016} }

There are several works characterizing the total-variation mixing time of a reversible Markov chain in term of natural probabilistic concepts such as stopping times and hitting times. In contrast, there is no known analog for the $L_{2}$ mixing time, $\tau_{2}$ (while there are sophisticated analytic tools to bound $ \tau_2$, in general they do not determine $\tau_2$ up to a constant factor and they lack a probabilistic interpretation). In this work we show that $\tau_2$ can be characterized up… CONTINUE READING

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SHOWING 1-10 OF 17 REFERENCES

## Reversible markov chains and random walks on

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Surprise probabilities in Markov chains

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL

## On sensitivity of uniform mixing times

VIEW 1 EXCERPT

## Characterization of cutoff for reversible Markov chains

VIEW 1 EXCERPT

## Mixing Times are Hitting Times of Large Sets

VIEW 2 EXCERPTS

## On the precision of the spectral profile

VIEW 1 EXCERPT