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directed polymer

ESAIM: Probability and Statistics (1)

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1 results

Directed polymer in random environment and last passage percolation *
Philippe Carmona
Journal:

ESAIM: Probability and Statistics / Volume 14 / 2010

Published online by Cambridge University Press:

29 October 2010, pp. 263-270

Print publication:

2010
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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.