The Partition Function of Log-Gases with Multiple Odd Charges
Abstract
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 $\beta$ 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 $\beta$-ensembles ($\beta$ = 1, 2, 4) to multicomponent ensembles, as well as to iterated integrals of more general determinantal integrands.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2021
- arXiv:
- arXiv:2105.14378
- Bibcode:
- 2021arXiv210514378W
- Keywords:
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- Mathematical Physics;
- Mathematics - Probability;
- 60G55 (Primary);
- 82D05 (Secondary);
- 15B52;
- 15A15;
- 15A69
- E-Print:
- 31 pages