Endpoint distribution of directed polymers in 1+1 dimensions

Details Endpoint distribution of directed polymers in 1+1 dimensions Endpoint distribution of directed polymers in 1+1 dimensions

2011-06-14

arxiv.org/abs/1106.2716v4

Mathematics

Probability

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Scientific paper

We give an explicit formula for the joint density of the max and argmax of
the Airy$_2$ process minus a parabola. The argmax has a universal distribution
which governs the rescaled endpoint for large time or temperature of directed
polymers in 1+1 dimensions.

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