Jani Virtanen (University of Reading) : Asymptotics of Toeplitz and related determinants with matrix-valued symbols

Lieu : Salle Kampé de Fériet, 1er étage, Bâtiment M2

Date : 29 Novembre 2024

Heure : 14h

Orateur : Jani Virtanen

Affiliation : University of Reading

Titre : Asymptotics of Toeplitz and related determinants with matrix-valued symbols

Résumé :

Toeplitz matrices are simple matrices constant along parallels to the main diagonal with the (j,k) entry given by f_{j-k}. When the entries are generated by the Fourier coefficients of a sufficiently nice smooth matrix-valued function, the asymptotic behavior of the determinants of the corresponding Toeplitz matrices is well understood (the Szegö-Widom theorem). Also, for scalar-valued functions that possess singularities, such as zeros, discontinuities, and root-type singularities, the asymptotics are well understood (the Fisher-Hartwig conjecture). However, very little is known about the case of matrix-valued functions that posses singularities and I will discuss the case of jumps and some of their applications to mathematical physics. I will also mention other related matrices, such as Toeplitz+Hankel matrices, and discuss their determinant asymptotics.