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CUTOFF FOR NON-BACKTRACKING RANDOM WALKS ON SPARSE RANDOM GRAPHS

Abstract : A finite ergodic Markov chain is said to exhibit cutoff if its distance to stationarity remains close to 1 over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Discovered in the context of card shuffling (Aldous-Diaconis, 1986), this phenomenon is now believed to be rather typical among fast mixing Markov chains. Yet, establishing it rigorously often requires a challengingly detailed understanding of the underlying chain. Here we consider non-backtracking random walks on random graphs with a given degree sequence. Under a general sparsity condition, we establish the cutoff phenomenon, determine its precise window, and prove that the (suitably rescaled) cutoff profile approaches a remarkably simple, universal shape.
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https://hal.archives-ouvertes.fr/hal-01141192
Contributor : Anna Ben-Hamou <>
Submitted on : Friday, April 10, 2015 - 5:35:40 PM
Last modification on : Friday, March 27, 2020 - 3:06:08 AM
Document(s) archivé(s) le : Tuesday, April 18, 2017 - 4:26:15 PM

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  • HAL Id : hal-01141192, version 1
  • ARXIV : 1504.02429

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Anna Ben-Hamou, Justin Salez. CUTOFF FOR NON-BACKTRACKING RANDOM WALKS ON SPARSE RANDOM GRAPHS. 2015. ⟨hal-01141192⟩

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