Reconstructing a large subset of a point set in R from random sparse distance information

Add to your list(s) Download to your calendar using vCal

• Julien Portier (Cambridge)
• Thursday 21 November 2024, 14:30-15:30
• MR12.

If you have a question about this talk, please contact ibl10.

Let $V$ be a set of $n$ points in $\mathbb{R}$, and let $\epsilon > 0$ be a small enough fixed constant. Suppose the distances between each pair of points are revealed according to an Erd\H{o}s-Rényi random graph $G(n,(1+\epsilon)/n)$, meaning that the distance between any two points is revealed independently with probability $p=\frac{1+\epsilon}{n}$. We show that, with high probability, this information is sufficient to reconstruct, up to isometry, a subset of $V$ of size $\Omega_{\epsilon}(n)$. This confirms a conjecture posed by Gir\~ao, Illingworth, Michel, Powierski, and Scott. Our approach involves proving certain structural properties of the $2$-core of $G(n,(1+\epsilon)/n)$, which can be of independent interest. This work is joint with Julian Sahasrabudhe.

This talk is part of the Combinatorics Seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• Combinatorics Seminar
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR12
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.