Averages of Exponentials from the point of view of Superintegrability

A. Morozov

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arXiv · 2601.20213

Averages of Exponentials from the point of view of Superintegrability

A. Morozov

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Abstract

We calculate Gaussian averages of arbitrary exponentials of the matrix variable $X$ with the help of superintegrability, which provides explicit expressions for Schur averages. As in the simpler cases the answer is expressed in terms of Laguerre polynomials, but in a somewhat sophisticated way. It involves triangular sum over partitions, with simple exponential factor and a complicated polynomial prefactor. Some ingredients of the formula are not found in full generality and there is still a room for further work.

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A. Morozov. 2026-01-28. Averages of Exponentials from the point of view of Superintegrability. https://arxiv.org/abs/2601.20213

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