Séminaire SPACE Tours
A Pfaffian Borodin-Okounkov FormulaPierre Lazag (IDP, Université de Tours)
Friday 17 October 2025 10:30 - Tours - E2 1180
Résumé :
The Borodin-Okounkov formula is an identity between a Toeplitz determinant of size N and a Fredholm determinant of an operator acting on l^2(N,N+1,N+2,...). This identity provides an equality between the expectation of a multiplicative functional for the Circular Unitary Ensemble on the one hand, and the the probability distribution of the largest part of a random partition under a Schur measure on the other hand. The original proof of Borodin and Okounkov relies on the Gessel formula expressing the distribution of the largest part of a random partition under a Schur measure as a Toeplitz determinant, together with a theorem by Okounkov stating that Schur measures are determinantal point processes. In this talk, I will review this proof of the Borodin-Okounkov formula and discuss its extension to the Pfaffian case by looking at Pfaffian Schur measures. This is an ongoing work with Alexander Bufetov.
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