Directed polymer in random environment and last passage percolation

Philippe Carmona (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

The sequence of random probability measures $\nu_n$ that gives a path of length $n$, $\unsur{n}$ 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.

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

Domaines: Probabilités [math.PR]

Philippe Carmona. Directed polymer in random environment and last passage percolation. ESAIM: Probability and Statistics, 2010, 14, pp.263--270. ⟨hal-00315297⟩