Paper detail

A Solvable Two-Charge Ensemble on the Circle

We introduce an ensemble consisting of logarithmically repelling charge one and charge two particles on the unit circle constrained so that the total charge of all particles equals $N$, but the proportion of each species of particle is allowed to vary according to a fugacity parameter. We identify the proper scaling of the fugacity with $N$ so that the proportion of each particle stays positive in the $N \rightarrow \infty$ limit. This ensemble forms a Pfaffian point process on the unit circle, and we derive the scaling limits of the matrix kernel(s) as a function of the interpolating parameter. This provides a solvable interpolation between the circular unitary and symplectic ensembles.