## Electronic Journal of Probability

### The Cusp-Airy process

#### 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 but their formula is not completely correct.

#### Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 57, 50 pp.

Dates
Accepted: 7 July 2016
First available in Project Euclid: 9 September 2016

https://projecteuclid.org/euclid.ejp/1473424498

Digital Object Identifier
doi:10.1214/16-EJP2

Mathematical Reviews number (MathSciNet)
MR3546394

Zentralblatt MATH identifier
1348.60008

#### Citation

Duse, Erik; Johansson, Kurt; Metcalfe, Anthony. The Cusp-Airy process. Electron. J. Probab. 21 (2016), paper no. 57, 50 pp. doi:10.1214/16-EJP2. https://projecteuclid.org/euclid.ejp/1473424498

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