Mixing time trichotomy in regenerating dynamic digraphs

Linking the mixing times of random walks on static and dynamic random graphs

“…Non-backtracking random walks on configuration models that with high probability are connected were studied in a series of papers [4,5,6], which culminated in a general framework for studying mixing times of non-backtracking random walks on dynamic random graphs subject to mild regularity conditions. Mixing of random walks on directed configuration models was treated in [16].…”

On the meeting of random walks on random DFA

“…(This condition translates into the constraint that a random DFA does not display multiple edges with the same origin-destination pair.) We impose this condition for the mere scope of importing without changes all the results in [BCS19,CQ21b], which are based on this assumption.…”

Mixing trichotomy for an Ehrenfest urn with impurities

“…To which extent is the cutoff phenomenon robust? In the last few years, similar questions have been investigated in [AGHH19,CQ21a,CQ21b,AGHHN22]. Despite the models in the aforementioned papers are quite different, they can all be framed into a setting in which the perturbed chain is affected by the competition of two different mixing mechanisms: on the one hand, the abrupt convergence to equilibrium of the original chain, while, on the other hand, a smooth decay to equilibrium arising as an effect of the perturbation.…”

“…Despite the models in the aforementioned papers are quite different, they can all be framed into a setting in which the perturbed chain is affected by the competition of two different mixing mechanisms: on the one hand, the abrupt convergence to equilibrium of the original chain, while, on the other hand, a smooth decay to equilibrium arising as an effect of the perturbation. Moreover, the models in [AGHH19, CQ21b,AGHHN22] share the common feature that the mixing stochastic process under investigation is not a Markov process itself, but rather a non-Markonian observable of a Markov process. A similar investigation, namely the analysis of mixing behavior of observables (or features or statistics) of Markov chains, has been recently performed in [W19a, W19b] in the context of card shuffling routines and related models.…”