Random skew plane partitions and the Pearcey process

2005/03/23 by Andrei Okounkov, Andreĭ Okounkov, Nicolai Reshetikhin +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #68R05 #82B05 #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #math-ph #math.CO #math.MP #msc:68R05 #msc:82B05

paper · pdf · doi:10.48550/arxiv.math/0503508

openalex publication_date 2005/03/23 · arxiv created 2005/04/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study random skew 3D partitions weighted by q^\textupvol and, specifically, the q→ 1 asymptotics of local correlations near various points of the limit shape. We obtain sine-kernel asymptotics for correlations in the bulk of the disordered region, Airy kernel asymptotics near a general point of the frozen boundary, and a Pearcey kernel asymptotics near a cusp of the frozen boundary.

Citations

• Random surfaces enumerating algebraic curves
• Differential Equations for Dyson Processes

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