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SUMMARY:M. E. Lakshmi Priya (Indian Institute of Science\, Bangalore)
DTSTART:20210215T090000Z
DTEND:20210215T094500Z
DTSTAMP:20260421T173225Z
UID:BPS/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BPS/21/">Ove
 rcrowding estimates for nodal volume of stationary Gaussian processes (SGP
 s) on R^d</a>\nby M. E. Lakshmi Priya (Indian Institute of Science\, Banga
 lore) as part of Bangalore Probability Seminar\n\n\nAbstract\nWe consider 
 centered SGPs on Euclidean spaces R^d and study their nodal volume in [0\,
 T]^d\, for T>0. From earlier studies\, we know the following statistics fo
 r nodal volume of SGPs under varying assumptions on their spectral measure
 s: expectation\, variance asymptotics\, CLT\, exponential concentration (o
 nly for d=1)\, and finiteness of moments. \n\nWe study the unlikely event 
 of overcrowding of the nodal set in [0\,T]^d\; this is the event that the 
 volume of the nodal set in [0\,T]^d is much larger than its expected value
 . Under some mild assumptions on the spectral measure\, we obtain estimate
 s for the overcrowding event's probability. We first get overcrowding esti
 mates for the zero count of SGPs on R. In higher dimensions\, we consider 
 Crofton's formula\, which gives the volume of the nodal set in terms of th
 e number of intersections of the nodal set with all lines in R^d. We discr
 etize this formula to get a more workable version of it and\, in a sense\,
  reduce the overcrowding problem in higher dimensions to the one-dimension
 al case.\n
LOCATION:https://researchseminars.org/talk/BPS/21/
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