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Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2022

Spectral gap and cutoff phenomenon for the Gibbs sampler of $\nabla\varphi$ interfaces with convex potential

Résumé

We consider the Gibbs sampler, or heat bath dynamics associated to log-concave measures on $\mathbb{R}^N$ describing $\nabla\varphi$ interfaces with convex potentials. Under minimal assumptions on the potential, we find that the spectral gap of the process is always given by $\mathrm{gap}_N=1-\cos(\pi/N)$, and that for all $\epsilon\in(0,1)$, its $\epsilon$-mixing time satisfies $T_N(\epsilon)\sim \frac{\log N}{2\mathrm{gap}_N}$ as $N\to\infty$, thus establishing the cutoff phenomenon. The results reveal a universal behavior in that they do not depend on the choice of the potential.

Dates et versions

hal-03004695 , version 1 (13-11-2020)

Identifiants

Citer

Pietro Caputo, Cyril Labbé, Hubert Lacoin. Spectral gap and cutoff phenomenon for the Gibbs sampler of $\nabla\varphi$ interfaces with convex potential. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2022, 58 (2), ⟨10.1214/21-AIHP1174⟩. ⟨hal-03004695⟩
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