Eynard-Mehta theorem, Schur process, and their pfaffian analogs
arXiv:math-ph/0409059 · doi:10.1007/s10955-005-7583-z
Abstract
We give simple linear algebraic proofs of Eynard-Mehta theorem, Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also discuss certain general properties of the spaces of all determinantal and Pfaffian processes on a given finite set.
AMSTeX, 21 pages, a new section added
References in corpus (7)
- Discrete polynuclear growth and determinantal processes
- Differential Equations for Dyson Processes
- Fluctuations of a one-dimensional polynuclear growth model in a half space
- A Limit Theorem for Shifted Schur Measures
- Non-intersecting, simple, symmetric random walks and the extended Hahn kernel
- Correlation functions of the shifted Schur measure
- Alpha-Pfaffian, pfaffian point process and shifted Schur measure
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