The Partition Function of LogGases with Multiple Odd Charges
Abstract
We use techniques in the shuffle algebra to present a formula for the partition function of a onedimensional loggas comprised of particles of (possibly) different integer charges at certain inverse temperature $\beta$ in terms of the Berezin integral of an associated nonhomogeneous 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 $\beta$ensembles ($\beta$ = 1, 2, 4) to multicomponent ensembles, as well as to iterated integrals of more general determinantal integrands.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2105.14378
 Bibcode:
 2021arXiv210514378W
 Keywords:

 Mathematical Physics;
 Mathematics  Probability;
 60G55 (Primary);
 82D05 (Secondary);
 15B52;
 15A15;
 15A69
 EPrint:
 31 pages