BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Reconstructing a large subset of a point set in R from random spar
 se distance information - Julien Portier (Cambridge)
DTSTART:20241121T143000Z
DTEND:20241121T153000Z
UID:TALK224788@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION: Let $V$ be a set of $n$ points in $\\mathbb{R}$\, and let $\\
 epsilon > 0$ be a small enough fixed constant. Suppose the distances betwe
 en each pair of points are revealed according to an Erd\\H{o}s-Rényi rand
 om graph $G(n\,(1+\\epsilon)/n)$\, meaning that the distance between any t
 wo points is revealed independently with probability $p=\\frac{1+\\epsilon
 }{n}$. We show that\, with high probability\, this information is sufficie
 nt to reconstruct\, up to isometry\, a subset of $V$ of size $\\Omega_{\\e
 psilon}(n)$. This confirms a conjecture posed by Gir\\~ao\, Illingworth\, 
 Michel\, Powierski\, and Scott. Our approach involves proving certain stru
 ctural properties of the $2$-core of $G(n\,(1+\\epsilon)/n)$\, which can b
 e of independent interest.\nThis work is joint with Julian Sahasrabudhe.
LOCATION:MR12
END:VEVENT
END:VCALENDAR