Elisha D. Wolff | Searcharxiv

arXiv2022

The Partition Function of Log-Gases with Multiple Odd Charges

We use techniques in the shuffle algebra to present a formula for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charges at certain inverse temperature $β$ in terms of the Berezin integral of an associated non-homogeneous alternating tensor. This generalizes previously known results by removing the restriction on the number of species of odd charge. Our methods provide a unified framework extending the de Bruijn integral identities from classical $β$-ensembles ($β$ = 1, 2, 4) to multicomponent ensembles, as well as to iterated integrals of more general determinantal integrands.

math-ph↗

arXiv2021

Constellation Ensembles and Interpolation in Ensemble Averages

We introduce constellation ensembles, in which charged particles on a line (or circle) are linked with charged particles on parallel lines (or concentric circles). We present formulas for the partition functions of these ensembles in terms of either the Hyperpfaffian or the Berezin integral of an appropriate alternating tensor. Adjusting the distances between these lines (or circles) gives an interpolation between a pair of limiting ensembles, such as one-dimensional $β$-ensembles with $β=K$ and $β=K^2$.

math-ph↗