Geodesic
Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
Okounkov, Andrei1 ; Reshetikhin, Nikolai1
1 Department of Mathematics, University of California at Berkeley, Evans Hall #3840, Berkeley, California 94720-3840
Journal of the American Mathematical Society, Tome 16 (2003) no. 3, pp. 581-603

Voir la notice de l'article provenant de la source American Mathematical Society

The Schur process is a time-dependent analog of the Schur measure on partitions studied by A. Okounkov in Infinite wedge and random partitions, Selecta Math., New Ser. 7 (2001), 57–81. Our first result is that the correlation functions of the Schur process are determinants with a kernel that has a nice contour integral representation in terms of the parameters of the process. This general result is then applied to a particular specialization of the Schur process, namely to random 3-dimensional Young diagrams. The local geometry of a large random 3-dimensional diagram is described in terms of a determinantal point process on a 2-dimensional lattice with the incomplete beta function kernel (which generalizes the discrete sine kernel). A brief discussion of the universality of this answer concludes the paper.
DOI : 10.1090/S0894-0347-03-00425-9

Okounkov, Andrei 1 ; Reshetikhin, Nikolai 1

1 Department of Mathematics, University of California at Berkeley, Evans Hall #3840, Berkeley, California 94720-3840 
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Okounkov, Andrei; Reshetikhin, Nikolai. Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram. Journal of the American Mathematical Society, Tome 16 (2003) no. 3, pp. 581-603. doi: 10.1090/S0894-0347-03-00425-9

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