Proof of the path localization conjecture for directed polymers

Abstract

It is a well-known open problem in the literature on random polymers to show that a directed polymer in random environment localizes around a favorite path at low temperature. A precise statement of this conjecture is formulated and proved in this article.

16 pages, 1 figure. To appear in Comm. Math. Phys

References in corpus (3)

• Strong disorder implies strong localization for directed polymers in a random environment
• Localization Transition for Polymers in Poissonian Medium
• Pinning Model with Heavy Tailed Disorder

Cited by in corpus (5)

• Full-path localization of directed polymers
• The geometric Burge correspondence and the partition function of polymer replicas
• Gaussian fluctuations for the directed polymer partition function for $d\ge 3$ and in the whole $L^2$-region
• Localization length of the $1+1$ continuum directed random polymer
• Localization and free energy asymptotics in disordered statistical mechanics and random growth models