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SUMMARY:Hunter Spink (Stanford)
DTSTART:20210729T180000Z
DTEND:20210729T190000Z
DTSTAMP:20260423T035717Z
UID:OLS/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/65/">Pro
 babilistic Littlewood-Offord anti-concentration results via model theory</
 a>\nby Hunter Spink (Stanford) as part of Online logic seminar\n\n\nAbstra
 ct\nAbstract: (Joint with Jacob Fox and Matthew Kwan) The classical Erdos-
 Littlewood-Offord theorem says that for any n nonzero vectors in $R^d$\, a
  random signed sum concentrates on any point with probability at most $O(n
 ^{-1/2})$. Combining tools from probability theory\, additive combinatoric
 s\, and model theory\, we obtain an anti-concentration probability of $n^{
 -1/2+o(1)}$ for any o-minimal set $S$ in $R^d$ (such as a hypersurface def
 ined by a polynomial in $x_1\,...\,x_n\,e^{x_1}\,...\,e^{x_n}$\, or a rest
 ricted analytic function) not containing a line segment. We do this by sho
 wing such o-minimal sets have no higher-order additive structure\, complem
 enting work by Pila on lower-order additive structure developed to count r
 ational and algebraic points of bounded height.\n
LOCATION:https://researchseminars.org/talk/OLS/65/
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