| Issue |
ESAIM: PS
Volume 14, 2010
|
|
|---|---|---|
| Page(s) | 263 - 270 | |
| DOI | https://doi.org/10.1051/ps:2008034 | |
| Published online | 29 October 2010 | |
Directed polymer in random environment and last passage percolation*
Laboratoire Jean Leray, UMR 6629 Université de Nantes, BP 92208, 44322 Nantes Cedex 03, France
http://www.math.sciences.univ-nantes.fr/~carmona
Corresponding author: Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
12
June
2008
Abstract
The sequence of random probability measures νn that gives a path of length n, 
times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform of the free energy of the associated directed polymer in a random environment.
Consequences on the asymptotics of the typical number of paths whose collected weight is above a fixed proportion are then drawn.
Mathematics Subject Classification: 60K37
Key words: Directed polymer / random environment / partition function / last passage percolation
The author acknowledges the support of the French Ministry of Education through the ANR BLAN07-2184264 grant.
© EDP Sciences, SMAI, 2010
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