Localization Transition for Polymers in Poissonian Medium

Abstract

We study a model of directed polymers in random environment in dimension $1+d$, given by a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogeneities, respectively the intensity parameter $\nu$ of the Poisson field and the temperature inverse $\beta$. Our results are: (i) fine information on the phase diagram, with quantitative estimates on the critical curve; (ii) pathwise localization at low temperature and/or large density; (iii) complete localization in a favourite corridor for large $\nu {\beta }^2$ and bounded $\beta$.

References in corpus (4)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Large deviation rate functions for the partition function in a log-gamma distributed random potential
• Asymmetric directed polymers in random environments

Cited by in corpus (10)

• Localization of directed polymers with general reference walk
• Limiting results for the free energy of directed polymers in random environment with unbounded jumps
• Proof of the path localization conjecture for directed polymers
• Brownian Polymers in Poissonian Environment: a survey
• A remark on the bound for the free energy of directed polymers in random environment in 1+2 dimension
• Directed polymers on infinite graphs
• Full-path localization of directed polymers
• Localization length of the $1+1$ continuum directed random polymer
• Zero temperature limit for the Brownian directed polymer among Poissonian disasters
• Localization and free energy asymptotics in disordered statistical mechanics and random growth models