Endpoint distribution of directed polymers in 1+1 dimensions

Authors:
  • GFGregorio Moreno Flores
    Gregorio Moreno Flores
  • JQJeremy Quastel
    Jeremy Quastel
  • DRDaniel Remenik
    Daniel Remenik
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Abstract
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.