Directed polymer in random environment and last passage percolation

2008/08/28 by Carmona, Philippe · 1 citation
#60K37 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0808.3842

Abstract

The sequence of random probability measures ν_n that gives a path of length n, \unsurn 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.

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