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The KPZ equation and the directed landscape | | Xuan Wu
; | | Date: |
2 Jan 2023 | | Abstract: | This paper studies the convergence of the narrow wedge solutions of the KPZ
equation to the Airy sheet and the direct landscape. Our main approach is
inspired by the polymer free energy interpretation of the KPZ equation. We
derive a simple inequality relating Busemann functions and quantiles of the
polymer measure (Lemma 4.6) and this is one of the main ingredients for proving
the convergence. Another main ingredient is Proposition 3.5, an identity for
the geometric RSK correspondence. | | Source: | arXiv, 2301.00547 | | Services: | Forum | Review | PDF | Favorites | |
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