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arXiv · 2309.04299

Siegel Brownian motion

Govind Menon·Tianmin Yu
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Abstract

We construct an analogue of Dyson Brownian motion in the Siegel half-space H that we term Siegel Brownian motion. Given \beta in (0,\infty], a stochastic flow for Z_t in H is introduced so that the law of the eigenvalues \lambda_t of the cross ratio matrix R(Z_t,iI_n) is determined by the Ito differential equation corresponds to stochastic gradient ascent of a function S. S turns out to be the log volume of isospectral orbit in H and can be understood as a Boltzmann entropy. In the limit \beta=\infty, the group orbits evolve by motion by minus a half times mean curvature.

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Govind Menon, Tianmin Yu. 2023-09-08. Siegel Brownian motion. https://arxiv.org/abs/2309.04299

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