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DTSTART:20230326T030000
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BEGIN:VEVENT
DTSTAMP:20240304T185315Z
UID:1696943700@ist.ac.at
DTSTART:20231010T151500
DTEND:20231010T161500
DESCRIPTION:Speaker: Andrew Campbell\nhosted by Laszlo Erdös\nAbstract: Re
cently\, a (growing) number of papers have described a surprising connecti
on between differential operators applied to (deterministic or random) pol
ynomials and sums of random matrices. These results have been primarily fo
cused polynomials with real roots where the related random matrices are He
rmitian. After briefly discussing the history and success of this approach
to real rooted polynomials we will consider the extension to polynomials
with complex roots. Many nice properties are lost when considering complex
roots\, and hence non-Hermitian matrices\, so we will specifically focus
on random polynomials with independent coefficients and single ring matric
es. We will discuss how free probability theory can connect sums of these
single ring matrices to derivatives of these polynomials. With this conn
ection in hand we will consider questions of stability and central limit
behavior of the roots under differentiation. Based on joint work with Sean
O’Rourke and David Renfrew.
LOCATION:Heinzel Seminar Room (I21.EG.101)\, Office Building West\, ISTA\,
ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Andrew Campbell: Fractional $R$-diagonal convolution\, truncated si
ngle ring matrices\, and dynamics of complex polynomial roots.
URL:https://talks-calendar.ista.ac.at/events/4476
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