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UID:4724@test.i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170315T143000
DTEND;TZID=Europe/Paris:20170315T160000
DTSTAMP:20210412T100738Z
URL:https://test.i2m.univ-amu.fr/events/projections-of-orbital-measures-sp
lines-and-determinantal-formulas/
SUMMARY:Projections of orbital measures\, splines and determinantal formula
s - Alexander Bufetov
DESCRIPTION:Let M be an Hermitian nxn matrix (over C) with the given spectr
um X. If we take the principal minor M_k of size kxk\, what will be the pr
opability of M_k to have the spectrum Y?\nFor the simplest case\, when k=1
\, the the observation by Okounkov yields that the distribution of the ele
ment M_11 is given by the B-spline with knots in the eigenvalues of M.\n\n
More recently\, Olshanski in 2013 and Faraut in 2014 showed that for arbit
rary k\nThe talk will be devoted to the discussion of these results\, and
their generalization to the case of anti-symmetric and Hamiltonian matrice
s\, obtained by the speaker in 2016.\n\nIf time permits\, we shall also tr
y to discuss how these formulas are connected with the Defosseux's determi
nantal point process on the eigenvalues of M and all its principal minors.
CATEGORIES:SÃ©minaire Processus DÃ©terminantaux (ERC IChaos)
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DTSTART:20161030T020000
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