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UID:www.tcs.tifr.res.in/event/1749
DTSTAMP:20260716T054232Z
SUMMARY:Spectral gap of nonreversible Markov chains
DESCRIPTION:Speaker: Aindrila Rakshit (TIFR)\n\nAbstract: \nWe define the s
 pectral gap of a Markov chain on a finite state space as the second-smalle
 st singular value of the generator of the chain\, generalizing the usual d
 efinition of spectral gap for reversible chains. We then define the relaxa
 tion time of the chain as the inverse of this spectral gap\, and show that
  this relaxation time can be characterized\, for any Markov chain\, as the
  time required for convergence of empirical averages. This relaxation time
  is related to the Cheeger constant and the mixing time of the chain throu
 gh inequalities that are similar to the reversible case\, and the path arg
 ument can be used to get upper bounds. Several examples are worked out. An
  interesting finding from the examples is that the time for convergence of
  empirical averages in nonreversible chains can often be substantially sma
 ller than the mixing time.\nBY SOURAV CHATTERJEE\, Stanford University (20
 25)\nThe Annals of Applied Probability\, 35(4)\, 2644–2677. https://d
 oi.org/10.1214/25-AAP2183\, https://arxiv.org/abs/2310.10876\n \n
URL:https://www.tcs.tifr.res.in/web/events/1749
DTSTART;TZID=Asia/Kolkata:20260716T163000
DTEND;TZID=Asia/Kolkata:20260716T173000
LOCATION:A-201 (STCS Seminar Room)
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