Endpoint distribution of directed polymers in 1+1 dimensions
arXiv:1106.2716 · doi:10.1007/s00220-012-1583-z
Abstract
We give an explicit formula for the joint density of the max and argmax of the Airy 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.
arXiv commentExpanded introduction
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- Multiplicative functionals on ensembles of non-intersecting paths
- Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble
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- A PDE hierarchy for directed polymers in random environments