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DTSTART:20180325T030000
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DTSTAMP:20191023T162251Z
UID:5af2c73c7bded335689193@ist.ac.at
DTSTART:20180524T164500
DTEND:20180524T180000
DESCRIPTION:Speaker: Dan Betea\nhosted by Laszlo ErdÃ¶s\nAbstract: We look
at various measures on partitions coming from combinatorial representation
theory: the so-called Schur measures and some variants. We are interested
in fluctuations of the largest part(s) of said partitions --- discrete ve
rsions of largest eigenvalues of random matrices. One gets the Airy 2 (Tra
cy--Widom) fluctuations in the original Schur measure corresponding to the
Baik--Deift--Johansson longest increasing subsequences theorem\; Airy 1 (
GOE) and GSE fluctuations for random involutions (Baik--Rains\; Ferrari\;
Imamura--Sasamoto\; Baik--Barraquand--Corwin-- Suidan\; Betea--Bouttier--N
ejjar--Vuletic\; Bisi--Zygouras)\; Airy 2 to 1 (along with a certain dual)
fluctuations for symplectic and orthogonal Schur measures recently studie
d by the author and for a related model of Bisi--Zygouras\; and finally fi
nite temperature Airy2/Tracy--Widom fluctuations (interpolating between Gu
mbel and regular Tracy--Widom\; between Edwards--Wilkinson and KPZ) for a
certain 'cylindric' version of the Baik--Deift--Johansson case (joint work
of the author and Jeremie Bouttier). All such measures can be treated uni
formly with the aid of fermionic Fock space (equivalently\, they are deter
minantal processes)\, as was first championed by Okounkov. Most if not all
results relate to last passage percolation problems in certain simple geo
metries. All results are inspired by and have continuous random matrix ana
logues. It is conjectured though remains unproven that each Airy-type dist
ribution described above is universal for the geometry in question: the so
-called KPZ universality.
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
T Austria
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Integrable measures on partitions and Airy limit processes
URL:https://talks-calendar.app.ist.ac.at/events/1245
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