Constellation Ensembles and Interpolation in Ensemble Averages

TL;DR

The paper introduces constellation ensembles, linking charged particles on lines or circles, and provides formulas for their partition functions, enabling interpolation between different ensemble types through distance adjustments.

Contribution

It presents a novel class of constellation ensembles and derives explicit formulas for their partition functions using Hyperpfaffian and Berezin integrals.

Findings

Formulas for partition functions in terms of Hyperpfaffian and Berezin integrals.

Interpolation between different beta-ensembles achieved by adjusting distances.

Framework for analyzing charged particle ensembles on lines and circles.

Abstract

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 $\beta$-ensembles with $\beta=K$ and $\beta=K^2$.