Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram

Abstract

Schur process is a time-dependent analog of the Schur measure on partitions studied in math.RT/9907127. 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.

35 pages, 7 figures, to appear in JAMS

References in corpus (5)

• Quantum Dilogarithm
• A variational principle for domino tilings
• Universality of the local spacing distribution in certain ensembles of hermitian Wigner matrices
• Local statistics of lattice dimers
• Non-intersecting Paths, Random Tilings and Random Matrices

Cited by in corpus (8)

• Scale Invariance of the PNG Droplet and the Airy Process
• Lectures on Integrable probability: Stochastic vertex models and symmetric functions
• Extreme boundary conditions and random tilings
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• Step fluctuations for a faceted crystal
• Determinantal probability measures
• Random turn walk on a half line with creation of particles at the origin
• Refined Wall-Crossing, Free Fermions and Crystal Melting