scholarly journals Directed polymers in a random environment with a defect line

2015 ◽  
Vol 20 (0) ◽  
Author(s):  
Kenneth Alexander ◽  
Gökhan Yıldırım
Keyword(s):  
Random Environment ◽  
Directed Polymers ◽  
Defect Line

scholarly journals Directed polymers in a random environment: path localization and strong disorder

Bernoulli ◽  
2003 ◽  
Vol 9 (4) ◽  
pp. 705-723 ◽  
Author(s):  
Francis Comets ◽  
Tokuzo Shiga ◽  
Nobuo Yoshida
Keyword(s):  
Random Environment ◽  
Directed Polymers ◽  
Strong Disorder

Brownian Directed Polymers in Random Environment

2004 ◽  
Vol 254 (2) ◽  
pp. 257-287 ◽  
Author(s):  
Francis Comets ◽  
Nobuo Yoshida
Keyword(s):  
Random Environment ◽  
Directed Polymers

scholarly journals Limiting Results for the Free Energy of Directed Polymers in Random Environment with Unbounded Jumps

2015 ◽  
Vol 161 (3) ◽  
pp. 577-597 ◽  
Author(s):  
Francis Comets ◽  
Ryoki Fukushima ◽  
Shuta Nakajima ◽  
Nobuo Yoshida
Keyword(s):  
Free Energy ◽  
Random Environment ◽  
Directed Polymers

scholarly journals Directed polymers in a random environment with heavy tails

2010 ◽  
Vol 64 (2) ◽  
pp. 183-204 ◽  
Author(s):  
Antonio Auffinger ◽  
Oren Louidor
Keyword(s):  
Random Environment ◽  
Heavy Tails ◽  
Directed Polymers

scholarly journals Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions

2020 ◽  
Vol 178 (1-2) ◽  
pp. 121-171
Author(s):  
Will FitzGerald ◽  
Jon Warren
Keyword(s):  
Brownian Motion ◽  
Invariant Measure ◽  
Random Environment ◽  
Finite Temperature ◽  
Directed Polymers ◽  
Partition Functions ◽  
Brownian Motions ◽  
Last Passage Percolation ◽  
Brownian Motion With Drift ◽  
Inverse Gamma

Abstract This paper proves an equality in law between the invariant measure of a reflected system of Brownian motions and a vector of point-to-line last passage percolation times in a discrete random environment. A consequence describes the distribution of the all-time supremum of Dyson Brownian motion with drift. A finite temperature version relates the point-to-line partition functions of two directed polymers, with an inverse-gamma and a Brownian environment, and generalises Dufresne’s identity. Our proof introduces an interacting system of Brownian motions with an invariant measure given by a field of point-to-line log partition functions for the log-gamma polymer.

Diffusion of directed polymers in a strong random environment

1996 ◽  
Vol 83 (3-4) ◽  
pp. 727-738 ◽  
Author(s):  
Peder Olsen ◽  
Renming Song
Keyword(s):  
Random Environment ◽  
Directed Polymers
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