Double-scaling limits of Toeplitz determinants and their applications

Analyse Fonctionnelle

Lieu:
Salle Kampé de Fériet M2
Orateur:
Jani Virtanen
Affiliation:
For sufficiently smooth symbols, Szegö’s theorems describe the asymptotic behavior of Toeplitz determinants.
Asymptotic expansions are also known for the determinants of Toeplitz matrices generated by Fisher-Hartwig symbols (functions that may possess zeros, integrable singularities and discontinuities). Suppose now that the symbol has an extra parameter t with the property that when t goes to zero, the number of Fisher-Hartwig singularities changes. By double-scaling limits of Toeplitz determinants we mean limits of the determinants when the size of the matrices goes to infinity and t goes to zero simultaneously. In this talk, I discuss the known results on double-scaling limits and their applications in random matrix theory.