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09 February 2025
 
  » arxiv » 1609.0298

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Intermediate disorder limits for multi-layer semi-discrete directed polymers
Mihai Nica ;
Date 1 Sep 2016
AbstractWe show that the partition function of the multi-layer semi-discrete directed polymer converges in the intermediate disorder regime to the partition function for the multi-layer continuum polymer introduced by O’Connell and Warren. This verifies, modulo a previously hidden constant, an outstanding conjecture proposed by Corwin and Hammond. A consequence is the identification of the KPZ line ensemble as logarithms of ratios of consecutive layers of the continuum partition function. Other properties of the continuum partition function, such as continuity, strict positivity and contour integral formulas to compute mixed moments, are also identified from this convergence result. The proof uses a coupling, which was first introduced by Quastel, Moreno Flores, and Remenik, and an extension of the methods used to prove similar results for purely discrete polymers.
Source arXiv, 1609.0298
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