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DTSTAMP:20241010T201427Z
UID:6690d89acd81a384206617@ist.ac.at
DTSTART:20241001T163000
DTEND:20241001T173000
DESCRIPTION:Speaker: Andrew Campbell\nhosted by Laszlo ErdÃ¶s\nAbstract: We
will discuss two conjectures for entire functions with real roots. The fi
rst\, referred to as Cosine Universality\, asserts that the roots become p
erfectly spaced in the limit of repeated differentiation\, under very mild
assumptions on the original function. The second conjecture\, known as He
rmite Universality\, asserts that for an even entire function $f$ certain
polynomials associated to $f$\, known as the Jensen polynomials\, should c
onverge to Hermite polynomials after an appropriate centering and re-scali
ng under the same assumptions as Cosine Universality. Specifically\, we wi
ll see the surprising role random matrix theory plays in proving these con
jectures for even functions. Using the recently developed theory of finite
free probability we will translate these universality principles into pro
babilistic limit theorems which are roughly equivalent to averaging sums o
f random matrices. This talk will serve as an introduction to finite free
probability. Based on joint work with Sean O'Rourke and David Renfrew.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
)\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Andrew Campbell: Finite free probability and universality principle
s for roots of entire functions
URL:https://talks-calendar.ista.ac.at/events/5236
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