Volume 14, 2010
|Page(s)||263 - 270|
|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
Corresponding author: Corresponding author: firstname.lastname@example.org
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
© EDP Sciences, SMAI, 2010
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