The Partition Function of Log-Gases with Multiple Odd Charges

@article{Wolff2022ThePF,
  title={The Partition Function of Log-Gases with Multiple Odd Charges},
  author={Elisha D. Wolff and John Wells},
  journal={Random Matrices: Theory and Applications},
  year={2022}
}
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… 
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Constellation ensembles and interpolation in ensemble averages
TLDR
It is shown that adjusting the distances between these lines (or circles) gives an interpolation between a pair of limiting ensembles, such as one-dimensional β -ensembles withβ = K and β = K 2 .

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