BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Dylan King (Wake Forest University)
DTSTART:20200605T200000Z
DTEND:20200605T202500Z
DTSTAMP:20260423T011238Z
UID:CANT2020/69
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/69/
 ">Distribution of missing sums in correlated sumsets</a>\nby Dylan King (W
 ake Forest University) as part of Combinatorial and additive number theory
  (CANT 2021)\n\n\nAbstract\nGiven a finite set of integers $A$\, its sumse
 t is $A+A:= \\{a_i+a_j \\mid \na_i\,a_j\\in A\\}$. We examine $|A+A|$ as a
  random variable\, where $A\\subset I_n = \n[0\,n-1]$\, the set of integer
 s from 0 to $n-1$\, so that each element of $I_n$ is \nin $A$ with a fixed
  probability $p \\in (0\,1)$. Martin and O'Bryant studied the \ncase in wh
 ich $p=1/2$ and found a closed form for $\\mathbb{E}[|A+A|]$. Lazarev\, \n
 Miller\, and O'Bryant extended the result to find a numerical estimate for
  \n$\\text{Var}(|A+A|)$ and bounds on $m_{n\\\,\;\\\,p}(k) := \\mathbb{P}(
 2n-1-|A+A|=k)$. \nTheir primary tool was a graph theoretic framework which
  we now generalize to \nprovide a closed form for $\\mathbb{E}[|A+A|]$ and
  $\\text{Var}(|A+A|)$ for all \n$p\\in (0\,1)$ and establish good bounds f
 or $\\mathbb{E}[|A+A|]$ and \n$m_{n\\\,\;\\\,p}(k)$. We extend the graph t
 heoretic framework originally introduced \nby Lazarev\, Miller\, and O'Bry
 ant to correlated sumsets $A+B$ where $B$ is \ncorrelated to $A$ by the pr
 obabilities $\\mathbb{P}(i\\in B \\mid i\\in A) = p_1$ \nand $\\mathbb{P}(
 i\\in B \\mid i\\not\\in A) = p_2$. We provide some preliminary\nresults t
 owards finding $\\mathbb{E}[|A+B|]$ and $\\text{Var}(|A+B|)$ using this \n
 framework. \n\nJoint work with Hung Chu Viet\, Noah Luntzlara\, Thomas Mar
 tinez\, Lily Shao\, \nChenyang Sun\,  Victor Xu\, and Steven J. Miller.\n
LOCATION:https://researchseminars.org/talk/CANT2020/69/
END:VEVENT
END:VCALENDAR