Gegenbauer polynomials and fluctuation properties of the one-dimensional Riesz gas

Peter J. Forrester

The Riesz gas in one-dimension consists of particles interacting via a pair potential, $\mathrm{sgn}(s)|x-x^{\prime }{|}^{-s}$, $s\ne 0$ and $-\log |x-x^{\prime }|$ for $s=0$. In the infinite dens…