Majorizing multiplicative cascades for directed polymers in random media

2005/10/25 by Francis Comets, Vincent Vargas, Comets, Francis +1 · 2 citations
Mathematics · Physics and Astronomy · #60J30 #60K35 #82A51 #82D30 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.math/0510525

openalex publication_date 2005/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we give upper bounds for the free energy of discrete polymers in random media. The bounds are given by the so-called generalized multiplicative cascades from the statistical theory of turbulence. For the polymer model, we derive that the quenched free energy is different from the annealed one in dimension 1, for any finite temperature and general environment. This implies localization of the polymer.

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