Gessel-Type Expansion for the Circular ${\hat{I}}^2$-Ensemble and Central Limit Theorem for the Sine-${\hat{I}}^2$ Process for ${\hat{I}}^2\le 2$

Sergei M. Gorbunov

We obtain a Gessel-type expansion in Jack polynomials for the expectations of multiplicative functionals in the circular ${\hat{I}}^2$-ensemble. As a consequence, we establish a Szegő-type…