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The Cusp-Airy Process
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2943-7006
(English)Manuscript (preprint) (Other academic)
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.

National Category
Natural Sciences
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-176650OAI: oai:DiVA.org:kth-176650DiVA: diva2:868187
Funder
Knut and Alice Wallenberg Foundation, 2010.0063
Note

QC 20151110

Available from: 2015-11-09 Created: 2015-11-09 Last updated: 2015-11-10Bibliographically approved
In thesis
1. On Uniformly Random Discrete Interlacing Systems
Open this publication in new window or tab >>On Uniformly Random Discrete Interlacing Systems
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns uniformly random discrete interlacing particle sys-tems and their connections to certain random lozenge tiling models. In par-ticular it contains the first derivation of a relatively unknown universal scalinglimit, which we call the Cusp-Airy process, of certain lozenge tiling modelsat a cusp point. In addition it contains a characterization of the geometryof the macroscopic behavior of uniformly random discrete interlaced parti-cle systems that, although not complete, shows many new and interestingfeatures.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. vii, 56 p.
Series
TRITA-MAT-A, 2015:12
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-176652 (URN)978-91-7595-732-6 (ISBN)
Public defence
2015-12-04, Sal D3, Lindstedtsvägen 5, KTH, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20151110

Available from: 2015-11-10 Created: 2015-11-09 Last updated: 2015-11-10Bibliographically approved

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Johansson, Kurt

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Citation style
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