Projections of orbital measures, splines and determinantal formulas

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Date/heure
Date(s) - 15/03/2017
14 h 30 min - 16 h 00 min

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Let M be an Hermitian nxn matrix (over C) with the given spectrum X. If we take the principal minor M_k of size kxk, what will be the propability of M_k to have the spectrum Y?

For the simplest case, when k=1, the the observation by Okounkov yields that the distribution of the element M_11 is given by the B-spline with knots in the eigenvalues of M.

More recently, Olshanski in 2013 and Faraut in 2014 showed that for arbitrary k 
The talk will be devoted to the discussion of these results, and their generalization to the case of anti-symmetric and Hamiltonian matrices, obtained by the speaker in 2016.

If time permits, we shall also try to discuss how these formulas are connected with the Defosseux’s determinantal point process on the eigenvalues of M and all its principal minors.

Olivier CHABROL
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