Ensemble Averages of Assorted Log-Gas Models
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Date
2022-10-04
Authors
Wolff, Elisha
Journal Title
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Publisher
University of Oregon
Abstract
We use techniques in the shuffle and exterior algebras to present the partition functions for several log-gas models in terms of either the Hyperpfaffian or the Berezin integral of an appropriate alternating tensor. Our methods generalize the de Bruijn integral identities from classical beta-ensembles (beta=1,2,4) to iterated integrals of more general determinantal integrands, such as those arising from multicomponent and constellation ensembles. In the latter case, adjusting the distances between parallel lines or concentric circles also gives an interpolation between the limiting ensembles, such as one-dimensional beta-ensembles with beta=K and beta=K^2.
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Keywords
Berezin Integral, Confluent Vandermonde, Hyperpfaffian, Partition Function, Pfaffian, Wronskian