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SUMMARY:Nick Cook (Duke)
DTSTART:20210122T173000Z
DTEND:20210122T183000Z
DTSTAMP:20260423T024553Z
UID:PatC/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PatC/24/">Un
 iversality for the minimum modulus of random trigonometric polynomials</a>
 \nby Nick Cook (Duke) as part of Probability and the City Seminar\n\n\nAbs
 tract\nWe consider the restriction to the unit circle of random degree-n p
 olynomials with iid normalized coefficients (Kac polynomials). Recent work
  of Yakir and Zeitouni shows that for Gaussian coefficients\, the minimum 
 modulus (suitably rescaled) follows a limiting exponential distribution. W
 e show this is a universal phenomenon\, extending their result to arbitrar
 y sub-Gaussian coefficients\, such as Rademacher signs. For discrete distr
 ibutions we must now deal with possible arithmetic structure in the polyno
 mial evaluated at different points of the circle. On "minor arcs" we obtai
 n strong comparisons with the Gaussian model by translating to a random wa
 lk in a high dimensional phase space\, and obtaining strong decay estimate
 s on characteristic functions\, while major arcs can be handled with crude
 r arguments. Based on joint work with Hoi Nguyen.\n
LOCATION:https://researchseminars.org/talk/PatC/24/
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