A probabilistic Weyl-law for perturbed Berezin-Toeplitz operators
Izak Oltman
TL;DR
This paper establishes a probabilistic Weyl-law for the spectrum of randomly perturbed Berezin-Toeplitz operators, extending previous results through advanced symbol calculus techniques.
Contribution
It generalizes Vogel's 2020 Weyl-law to a probabilistic setting for perturbed Berezin-Toeplitz operators using a novel exotic symbol calculus.
Findings
Proves a probabilistic Weyl-law for perturbed Berezin-Toeplitz operators
Extends Vogel's 2020 spectral result to a probabilistic framework
Utilizes a new exotic symbol calculus for the proof
Abstract
This paper proves a probabilistic Weyl-law for the spectrum of randomly perturbed Berezin-Toeplitz operators, generalizing a result proven by Martin Vogel in 2020. This is done following Vogel's strategy using an exotic symbol calculus developed by the author in a recent paper.
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Taxonomy
TopicsRandom Matrices and Applications · Holomorphic and Operator Theory · Geometric Analysis and Curvature Flows