Majorizing multiplicative cascades for directed polymers in random media

TL;DR

This paper introduces upper bounds for the free energy of directed polymers in random media using generalized multiplicative cascades, revealing localization phenomena in one-dimensional models at any temperature.

Contribution

It applies generalized multiplicative cascades to derive bounds on free energy, demonstrating localization in 1D directed polymers at all temperatures.

Findings

Quenched free energy differs from annealed in 1D

Localization occurs in 1D at any temperature

Upper bounds are established via multiplicative cascades

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.