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.
Simon,Orthogonal Polynomials on the Unit Circle, Part 1: Classical Theory, AMS Colloquium Series, vol
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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.