## Electronic Journal of Probability

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

### The Cusp-Airy process

Erik Duse, Kurt Johansson, and Anthony Metcalfe

#### 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**

Received: 1 February 2016

Accepted: 7 July 2016

First available in Project Euclid: 9 September 2016

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1214/16-EJP2

**Mathematical Reviews number (MathSciNet)**

MR3546394

**Zentralblatt MATH identifier**

1348.60008

**Subjects**

Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

**Keywords**

discrete interlacing systems random tiling process scaling limit new determinantal point process

**Rights**

Creative Commons Attribution 4.0 International License.

#### 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