Hydrodynamic limit and cutoff for the biased adjacent walk on the simplex
Labbé, Cyril; Petit, Enguerand (2022), Hydrodynamic limit and cutoff for the biased adjacent walk on the simplex. https://basepub.dauphine.psl.eu/handle/123456789/23112
TypeDocument de travail / Working paper
Series titleCahiers du CEREMADE
MetadataShow full item record
Laboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We investigate the asymptotic in N of the mixing times of a Markov dynamics on N−1 ordered particles in an interval. This dynamics consists in resampling at independent Poisson times each particle according to a probability measure on the segment formed by its nearest neighbours. In the setting where the resampling probability measures are symmetric, the asymptotic of the mixing times were obtained and a cutoff phenomenon holds. In the present work, we focus on an asymmetric version of the model and we establish a cutoff phenomenon. An important part of our analysis consists in the derivation of a hydrodynamic limit, which is given by a non-linear Hamilton-Jacobi equation with degenerate boundary conditions.
Subjects / KeywordsMixing time; Cutoff; Adjacent walk; Hydrodynamic limit; Hamilton-Jacobi equation
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