Proof of the path localization conjecture for directed polymers
arXiv:1806.04220 · doi:10.1007/s00220-019-03533-1
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