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.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01141192
Contributeur : Anna Ben-Hamou <>
Soumis le : vendredi 10 avril 2015 - 17:35:40
Dernière modification le : lundi 29 mai 2017 - 14:23:49
Document(s) archivé(s) le : mardi 18 avril 2017 - 16:26:15

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

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UPMC | PMA | INSMI | USPC

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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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