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The Cutoff Phenomenon in Reversible Markov Chains

Eftekhari, Hamid | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48570 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Zohuri Zangeneh, Bijan
  7. Abstract:
  8. A sequence of Markov chains is said to exhibit (total variation) cutoff if the convergence to stationarity in total variation distance is abrupt. We consider reversible lazy chains. We prove a necessary and sufficient condition for the occurrence of the cutoff phenomena in terms of concentration of hitting time of “worst” (in some sense) sets of stationary measure at least , for some ... (0; 1). As an application of these methods, we prove that a sequence of lazy chains on finite trees exhibits cutoff if and only if the product of the mixing time and the spectral gap tends to
  9. Keywords:
  10. Mixing Time ; Cutoff Phenomenon ; Reversible Markov Chain ; Hitting Time ; Maximal Ineqalities ; Finite Tree