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UID:5b63097e-5475-45a4-acbc-ab9d48cfa684@nexttoyou
DTSTAMP:20261105T160144Z
DTSTART:20261106T200000Z
DTEND:20261106T210000Z
SUMMARY:Probability Seminar: Carl Mueller\, University of Rochester
LOCATION:Hylan Building 1106a\, Hylan Building\, Rochester\, NY 14620
DESCRIPTION:VALLEYS OF THE STOCHASTIC HEAT EQUATION\n\nThis is joint work 
 with Mathew Joseph\, Kunwoo Kim\, and Davar Khoshnevisan.\n\nIntermittenc
 y is a well-studied property of the stochastic heat equation. Namely\, fo
 r large time\, the solution is dominated by tall peaks separated by large
  valleys where the solution is small. The behavior of the peaks has attra
 cted the most attention\, and not many results deal with the valleys.\n\n
 In earlier work\, Kunwoo Kim\, Davar Khoshnevisan and I considered valley
 s of the stochastic heat equation in on the real line\, with a nonlinear 
 term multiplying white noise. We showed that as time t grows\, the valley
 s become wider at least at an exponential rate with exponent a constant t
 imes t to the 1/3. Also\, the supremum of the solution within the valley 
 vanishes at least at an exponential rate\, with exponent a constant times
  t to the -1/3.\n\nExperts believed that the 1/3 which appears in the exp
 onentials could be replaced by 1. But due to the nonlinear coefficient mu
 ltiplying the noise\, integrable probability cannot be applied. With the 
 help of Mathew Joseph\, we show that 1/3 can indeed be replaced by 1. We 
 also extend this result to higher dimensions\, with white noise replaced 
 by colored noise that is sufficiently strong in a way that we will explai
 n.\n\nhttp://next-to-u.app/events/5b63097e-5475-45a4-acbc-ab9d48cfa684
URL:http://next-to-u.app/events/5b63097e-5475-45a4-acbc-ab9d48cfa684
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