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arXiv · 1510.02057

The Cusp-Airy Process

Erik Duse·Kurt Johansson·Anthony Metcalfe
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Abstract

At a typical cusp point of the disordered region in a random tiling model we expect to see a determinantal process called the Pearcey process in the appropriate scaling limit. However, in certain situations another limiting point process appears that we call the Cusp-Airy process, which is a kind of two sided extension of the Airy kernel point process. We will study this problem in a class of random lozenge tiling models coming from interlacing particle systems. The situation was briefly studied previously by Okounkov and Reshetikhin under the name cuspidal turning point.

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Erik Duse, Kurt Johansson, Anthony Metcalfe. 2015-11-30. The Cusp-Airy Process. https://arxiv.org/abs/1510.02057

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