Introduces a two-color lift of the shifted Schur measure on pairs of partitions and derives its normalization, marginals, transition kernel, and independence of color volumes.
Correlation functions of the shifted Schur measure
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The shifted Schur measure introduced by Tracy and Widom is a measure on the set of all strict partitions, which is defined by Schur $Q$-functions. The main aim of this paper is to calculate the correlation function of this measure, which is given by a pfaffian. As an application, we prove that a limit distribution of $\lambda_j$'s with respect to a shifted version of the Plancherel measure for symmetric groups is identical with the corresponding distribution of the original Plancherel measure. Further we give expressions of the mean value and the variance of the size of a partition with respect to the measure defined by Hall-Littlewood functions.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Defines shifted t-Schur weight via modified odd operator on strict partitions, derives normalization, Pfaffian correlation kernel, Fredholm Pfaffian for largest part, and size cumulants, with positive measure for t equals negative q.
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A Two-Color Lift of the Shifted $t$-Schur Measure
Introduces a two-color lift of the shifted Schur measure on pairs of partitions and derives its normalization, marginals, transition kernel, and independence of color volumes.