Endpoint distribution of directed polymers in 1+1 dimensions
Gregorio Moreno Flores, Jeremy Quastel, Daniel Remenik
TL;DR
This paper derives an explicit formula for the joint distribution of the maximum and argmax of the Airy$_2$ process minus a parabola, revealing universal properties of directed polymers' endpoints in 1+1 dimensions.
Contribution
It provides a new explicit formula for the joint density of the maximum and argmax of the Airy$_2$ process, advancing understanding of directed polymers' endpoint distributions.
Findings
The argmax distribution is universal for large time or temperature.
The joint density formula links Airy processes to directed polymer endpoints.
Universal behavior observed in the rescaled endpoint distribution.
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.
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