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Almost sure Weyl asymptotics for non-selfadjoint Toeplitz operators

Date: Thursday, October 24, 2019 16:00 - 18:00
Speaker: Martin Vogel (IST Austria)
Location: Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Laszlo Erdös

Abstract:

The spectra of nonselfadjoint linear operators can be very unstable and sensitive to small perturbations. This phenomenon is usually referred to as "pseudospectral effect". To explore this spectral instability we study the spectra of small random perturbations of non-selfadjoint operators in the case of Toeplitz matrices and in the case of the Toeplitz quantization of complex-valued functions on the torus. We show that almost surely the eigenvalues follow a Weyl law. (Partly based on joint work with J. Sjstrand)
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