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Directed polymer in random environment and last passage percolation*
Published online by Cambridge University Press: 29 October 2010
Abstract
The sequence of random probability measures ν n that gives a path of length n, $\frac{1}{n}$ 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.
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- Research Article
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- © EDP Sciences, SMAI, 2010
Footnotes
The author acknowledges the support of the French Ministry of Education through the ANR BLAN07-2184264 grant.
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