Almost sure Weyl asymptotics for non-selfadjoint Toeplitz operators

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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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