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Directed polymer in random environment and last passage percolation*

Published online by Cambridge University Press:  29 October 2010

Philippe Carmona
Philippe Carmona*
Affiliation:
Laboratoire Jean Leray, UMR 6629 Université de Nantes, BP 92208, 44322 Nantes Cedex 03, France
*
Corresponding author: philippe.carmona@math.univ-nantes.fr
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Abstract

The sequence of random probability measures νn 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.

Keywords

Directed polymerrandom environmentpartition functionlast passage percolation
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 14 , 2010 , pp. 263 - 270
Copyright
© EDP Sciences, SMAI, 2010

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Footnotes

*

The author acknowledges the support of the French Ministry of Education through the ANR BLAN07-2184264 grant.

References

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