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}
}
  • Jonathan Hermon, Yuval Peres
  • 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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