Geodesic
Directed polymer in random environment and last passage percolation
ESAIM: Probability and Statistics, Tome 14 (2010), pp. 263-270

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The sequence of random probability measures νn that gives a path of length n, 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.

DOI : 10.1051/ps:2008034
Classification : 60K37
Keywords: directed polymer, random environment, partition function, last passage percolation 
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     author = {Carmona, Philippe},
     title = {Directed polymer in random environment and last passage percolation},
     journal = {ESAIM: Probability and Statistics},
     pages = {263--270},
     publisher = {EDP-Sciences},
     volume = {14},
     year = {2010},
     doi = {10.1051/ps:2008034},
     mrnumber = {2779483},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2008034/}
}
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Carmona, Philippe. Directed polymer in random environment and last passage percolation. ESAIM: Probability and Statistics, Tome 14 (2010), pp. 263-270. doi: 10.1051/ps:2008034

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