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Displaying similar documents to “Distances in random graphs with finite mean and infinite variance degrees.”

Directed polymer in random environment and last passage percolation

Philippe Carmona (2010)

ESAIM: Probability and Statistics

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