Directed polymer in random environment and last passage percolation

Philippe Carmona

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

Mots clés: Directed polymer; random environment; partition function; last passage percolation

Philippe Carmona. Directed polymer in random environment and last passage percolation. ESAIM: Probability and Statistics, 2010, 14, pp.263-270. ⟨10.1051/ps:2008034⟩. ⟨hal-00637022⟩