Shifted Schur process and asymptotics of large random strict plane partitions

Abstract

In this paper we define the shifted Schur process as a measure on sequences of strict partitions. This process is a generalization of the shifted Schur measure introduced in [TW] and [Mat] and is a shifted version of the Schur process introduced in [OR]. We prove that the shifted Schur process defines a Pfaffian point process. We further apply this fact to compute the bulk scaling limit of the correlation functions for a measure on strict plane partitions which is an analog of the uniform measure on ordinary plane partitions. As a byproduct, we obtain a shifted analog of the famous MacMahon's formula.

AMSTex, 48 pages, 12 figures

References in corpus (1)

• Discrete polynuclear growth and determinantal processes

Cited by in corpus (10)

• Lectures on Integrable probability: Stochastic vertex models and symmetric functions
• The periodic Schur process and free fermions at finite temperature
• A Macdonald refined topological vertex
• Pfaffian structures and certain solutions to BKP hierarchies II. Multiple integrals
• Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures
• Random Strict Partitions and Determinantal Point Processes
• Pfaffian Stochastic Dynamics of Strict Partitions
• A generalization of MacMahon's formula
• (q,t)-hook formula for Birds and Banners
• Plane overpartitions and cylindric partitions