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Correlation function of Schur process with application to local geometry of a random 3-dimensional Young Diagram (2003)
| Content Provider | CiteSeerX |
|---|---|
| Author | Reshetikhin, Nikolai Okounkov, Andrei |
| Abstract | Schur process is a time-dependent analog of the Schur measure on partitions studied in [16]. 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. |
| File Format | |
| Publisher Date | 2003-01-01 |
| Access Restriction | Open |
| Subject Keyword | Large Random 3-dimensional Diagram Determinantal Point Process Brief Discussion Particular Specialization Random 3-dimensional Young Diagram Nice Contour Integral Representation Discrete Sine Kernel Schur Process Local Geometry 3-dimensional Young Diagram General Result 2-dimensional Lattice Incomplete Beta Function Kernel First Result Time-dependent Analog Correlation Function Schur Measure |
| Content Type | Text |
