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SUMMARY:CENTRAL LIMIT THEOREMS AND THE GEOMETRY OF POLYNOMIALS - Julian Sa
 hasrabudhe (Cambridge)
DTSTART:20191112T151500Z
DTEND:20191112T161500Z
UID:TALK134098@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Let X ∈ {0\, . . . \, n} be a random variable with standard 
 deviation σ and let f_X be its probability generating function. Pemantle 
 conjectured that if σ is large and f_X has no roots close to 1 in the com
 plex plane then X must approximate a normal distribution. In this talk\, I
  will discuss a complete resolution of Pemantle’s conjecture. I shall al
 so mention a how these ideas can be used to prove a multivariate central l
 imit theorem for strong Rayleigh distributions\, thereby resolving a conje
 cture of Gosh\, Liggett and Pemantle. This talk is based on joint work wit
 h Marcus Michelen.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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