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UID:20250918T001425EDT-37247WhTDN@132.216.98.100
DTSTAMP:20250918T041425Z
DESCRIPTION:Title: Random matrices and the Gaussian multiplicative chaos on
  the line\n	\n	Abstract: The Gaussian multiplicative chaos is a relatively n
 ew universal object in probability that has many interesting geometric pro
 perties.\n\nThe characteristic polynomial of many classes of random matric
 es is\, in many cases conjecturally\, one class of finite approximation to
  these random measures. Great progress has been made on showing the random
  matrices from specific ``circular ensembles’’ converge to the GMC. Likewi
 se\, some progress has been made for unitarily—invariant random matrices. 
 We show some new partial progress in showing the 'Gaussian beta—ensemble' 
 has a GMC limit. This we do by using the representation of its characteris
 tic polynomial as an entry in a product of independent random two--by--two
  matrices. For a point z in the complex plane\, at which the transfer matr
 ix is to be evaluated\, this product of transfer matrices splits into thre
 e independent factors\, each of which can be understood as a different dyn
 amical system in the complex plane. Using this\, we show that the characte
 ristic polynomial is always represented as product of at most three terms\
 , two of which are exponentials of Gaussian fields and one of which is the
  stochastic Airy function\, up to vanishing multiplicative errors. Suffici
 ently far into the complex plane\, it can be represented using only one. A
 t a point z at the spectral edge\, there are two. At a point z in the bulk
  of the spectrum\, all three are necessary to describe the characteristic 
 polynomial. Joint work with Gaultier Lambert.\n
DTSTART:20191009T190000Z
DTEND:20191009T200000Z
LOCATION:Room 1205\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Elliot Paquette (Ohio State)
URL:/mathstat/channels/event/elliot-paquette-ohio-stat
 e-301320
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