# 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}
}
• Published 2016
• Mathematics
• 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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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 17 REFERENCES

## Reversible markov chains and random walks on

• David Aldous, Jim Fill
• 2002
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Surprise probabilities in Markov chains

• Mathematics, Computer Science
• SODA
• 2015
VIEW 2 EXCERPTS
HIGHLY INFLUENTIAL

## On sensitivity of uniform mixing times

VIEW 1 EXCERPT

## Sensitivity of Mixing Times in Eulerian Digraphs

• Mathematics, Computer Science
• SIAM J. Discrete Math.
• 2018

## Characterization of cutoff for reversible Markov chains

• Mathematics
• SODA 2015
• 2015
VIEW 1 EXCERPT

## Sensitivity of mixing times

• Mathematics
• 2013

## Mixing Times are Hitting Times of Large Sets

• Mathematics
• 2011
VIEW 2 EXCERPTS

## On Reverse Hypercontractivity

• Mathematics
• 2011

## Markov Chains and Mixing Times

• Mathematics
• 2008

## On the precision of the spectral profile

VIEW 1 EXCERPT