Derives Gessel-type Jack polynomial expansion for circular beta-ensemble expectations, yielding Szego limit theorem for H^{1/2} functions and Soshnikov-type CLT for sine-beta process when beta <= 2.
Strahov,Thez-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel, Advances in Mathematics224:1 (2010), 130-168
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Gessel-Type Expansion for the Circular $\beta$-Ensemble and Central Limit Theorem for the Sine-$\beta$ Process for $\beta\le 2$
Derives Gessel-type Jack polynomial expansion for circular beta-ensemble expectations, yielding Szego limit theorem for H^{1/2} functions and Soshnikov-type CLT for sine-beta process when beta <= 2.