Random Skew Plane Partitions and the Pearcey Process

By A. Okounkov, N. Reshetikhin. 2005

166 citations recorded by the source corpus.

We study random skew 3D partitions weighted by qvol 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.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7d2b95fce086ac4bc473769e08fcc4067b32845c

How researchers see this paper

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In Geometry and Topology

1. C. Vafa
2. Amer Iqbal
3. Balázs Szendrői
4. C. Kozçaz
5. R. Pandharipande
6. Jim Bryan
7. Marcos Mariño
8. A. Kirillov

In Mathematical Physics

1. Amer Iqbal
2. C. Kozçaz
3. C. Vafa
4. Balázs Szendrői
5. R. Pandharipande
6. Jim Bryan
7. Marcos Mariño
8. A. Kirillov

In Statistics and Probability

1. C. Kozçaz
2. C. Vafa
3. Amer Iqbal
4. A. Kirillov

Citations in the corpus

• Motivic degree zero Donaldson–Thomas invariants (2009, result): “Motivated by work of Okounkov and Reshetikhin [31], in a recent paper [19], Iqbal–Kozçaz–Vafa discussed a family of q-deformations of this formula.”
• The refined topological vertex (2007, methodology): “1 >m>vi , (130) x+ ui−1 2 x− ui+1 2 = q−1 ui , x− vi−1 2 x+ vi+1 2 = qv i , x− m x− m+1 = qm+1 2 , m<v1 or vi+1 −1 >m>ui . The generating function of the 3D partitions is then given by [21] Z3D(q) = X π Y a∈Z q|ηa| a = h0| Y0 k=−∞ Γ−(x + −k+ 1 2 ) Y∞ k=1 Γ+(x − −k+ 2 )|0i (131) = Y∞ k”
• The Birth of a Random Matrix (2006, methodology): “The results of [19], [18] show these correlation functions are determinantal: ρ t 1 ,b 1 . . . ρ t n ,b n = det K((t i , h i ), (t j , h j )) 1≤i,j≤n .”