2015/10/07 by Erik Duse, Duse, Erik, Kurt Johansson +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1510.02057
50 pages, 36 figures
arxiv created 2015/11/30 · arxiv updated 2015/12/01
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.