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Spectral gap and cutoff phenomenon for the Gibbs sampler of ∇φ interfaces with convex potential

Caputo, Pietro; Labbé, Cyril; Lacoin, Hubert (2020), Spectral gap and cutoff phenomenon for the Gibbs sampler of ∇φ interfaces with convex potential. https://basepub.dauphine.psl.eu/handle/123456789/22329

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03004695
Date
2020
Series title
Cahier de recherche du CEREMADE
Pages
38
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Author(s)
Caputo, Pietro
Dipartimento di Matematica [Roma TRE]
Labbé, Cyril
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lacoin, Hubert
Dipartimento di Matematica [Roma TRE]
Abstract (EN)
We consider the Gibbs sampler, or heat bath dynamics associated to log-concave measures on RN describing ∇φ interfaces with convex potentials. Under minimal assumptions on the potential, we find that the spectral gap of the process is always given by gapN=1−cos(π/N), and that for all ϵ∈(0,1), its ϵ-mixing time satisfies TN(ϵ)∼logN2gapN as N→∞, thus establishing the cutoff phenomenon. The results reveal a universal behavior in that they do not depend on the choice of the potential.
Subjects / Keywords
Spectral gap; Mixing time; Cutoff