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SUMMARY:Nicholas Cook (Duke University)
DTSTART:20210301T200000Z
DTEND:20210301T210000Z
DTSTAMP:20260423T035931Z
UID:paw/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/paw/21/">Uni
 versality for the minimum modulus of random trigonometric polynomials</a>\
 nby Nicholas Cook (Duke University) as part of Probability and Analysis We
 binar\n\n\nAbstract\nWe consider the restriction to the unit circle of ran
 dom degree-n polynomials with iid coefficients (Kac polynomials). Recent w
 ork of Yakir and Zeitouni shows that for Gaussian coefficients\, the minim
 um modulus (suitably rescaled) follows a limiting exponential distribution
 . We show this is a universal phenomenon\, extending their result to arbit
 rary sub-Gaussian coefficients\, such as Rademacher signs. Our approach re
 lates the joint distribution of small values at several angles to that of 
 a random walk in high-dimensional phase space\, for which we obtain strong
  central limit theorems. The case of discrete coefficients is particularly
  challenging as the distribution is then sensitive to arithmetic structure
  among the angles. Based on joint work with Hoi Nguyen.\n
LOCATION:https://researchseminars.org/talk/paw/21/
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