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The Cusp-Airy process
KTH Royal Inst Technol, Stockholm, Sweden.
KTH Royal Inst Technol, Stockholm, Sweden.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 21, 1-50 p., 57Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2016. Vol. 21, 1-50 p., 57
Keyword [en]
discrete interlacing systems, random tiling process, scaling limit, new determinantal point process
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-329551DOI: 10.1214/16-EJP2ISI: 000396611400016OAI: oai:DiVA.org:uu-329551DiVA: diva2:1149931
Available from: 2017-10-17 Created: 2017-10-17 Last updated: 2017-10-17Bibliographically approved

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