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UID:10fc9d0ff95c45c6e18d3d002b4f3055
CATEGORIES:Symmetric Functions & Probability Theory Seminar
CREATED:20251014T153427
SUMMARY:On the edge expansion of random polytopes
LOCATION:Hill 705
DESCRIPTION:A $0/1$-polytope in $mathbb{R}^n$ is the convex hull of a subset of ${0,1}^
 n$. The graph of a polytope $P$ is the graph whose vertices are the zero-di
 mensional faces of $P$ and whose edges are the one-dimensional faces of $P$
 . A conjecture of Mihail and Vazirani states that the edge expansion of the
  graph of every $0/1$-polytope is at least one. In this talk, we study a ra
 ndom version of the problem, where the polytope is generated by selecting v
 ertices of ${0,1}^n$ independently at random with probability $pin (0,1)$. 
 Improving earlier results, we show that, for any $pin (0,1)$, with high pro
 bability the edge expansion of the random $0/1$-polytope is bounded from be
 low by an absolute constant.\nThis is joint work with Asaf Ferber, Michael 
 Krivelevich, and Wojciech Samotij.\n
X-ALT-DESC;FMTTYPE=text/html:<p>A $0/1$-polytope in $mathbb{R}^n$ is the convex hull of a subset of ${0,
 1}^n$. The graph of a polytope $P$ is the graph whose vertices are the zero
 -dimensional faces of $P$ and whose edges are the one-dimensional faces of 
 $P$. A conjecture of Mihail and Vazirani states that the edge expansion of 
 the graph of every $0/1$-polytope is at least one. In this talk, we study a
  random version of the problem, where the polytope is generated by selectin
 g vertices of ${0,1}^n$ independently at random with probability $pin (0,1)
 $. Improving earlier results, we show that, for any $pin (0,1)$, with high 
 probability the edge expansion of the random $0/1$-polytope is bounded from
  below by an absolute constant.</p><p>This is joint work with Asaf Ferber, 
 Michael Krivelevich, and Wojciech Samotij.</p>
CONTACT: Marcelo Sales (UC Irvine)
DTSTAMP:20260908T114904
DTSTART;TZID=America/New_York:20251022T104500
DTEND;TZID=America/New_York:20251022T234500
SEQUENCE:0
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