Convergence time to equilibrium of the metropolis dynamics for the GREM
| Autor: | A. M. B. Nascimento, Luiz Renato Fontes |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Convex analysis
Random energy model Probability (math.PR) Markov process Poincaré inequality Inverse Statistical and Nonlinear Physics 01 natural sciences 010305 fluids & plasmas symbols.namesake 0103 physical sciences Path (graph theory) Convergence (routing) FOS: Mathematics symbols Applied mathematics Spectral gap 60K35 82B44 82C44 82D30 MECÂNICA ESTATÍSTICA 010306 general physics Mathematics - Probability Mathematical Physics Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | We study the convergence time to equilibrium of the Metropolis dynamics for the Generalized Random Energy Model with an arbitrary number of hierarchical levels, a finite and reversible continuous-time Markov process, in terms of the spectral gap of its transition probability matrix. This is done by deducing bounds to the inverse of the gap using a Poincar\'e inequality and a path technique. We also apply convex analysis tools to give the bounds in the most general case of the model. Comment: 22 pages |
| Databáze: | OpenAIRE |
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