Directed polymer in random environment and last passage percolation

Philippe Carmona

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arXiv · 0808.3842

Directed polymer in random environment and last passage percolation

Philippe Carmona

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Abstract

The sequence of random probability measures $ν_n$ 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.

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Philippe Carmona. 2008-08-28. Directed polymer in random environment and last passage percolation. https://arxiv.org/abs/0808.3842

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