Metric distortion of random spaces

Abstract: We consider a random set in the unit circle. Is the induced discrete metric of the set closer to that of another independent random set or to the evenly spaced set of the same cardinality? We measure the distortion by looking at the smallest bi-Lipschitz norm of all the bijections between the two sets. Since the distortion between two random sets has infinite expectation, the talk will focus on the median. We show that two random sets have "typically" smaller distortion than a random set and an evenly spaced set.

analysis of PDEsmetric geometry

Audience: researchers in the topic

Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

If you are interested in giving a talk, please let one of the organizers know. Also, please suggest speakers which you would like to hear talk. Most talks are 50 minutes, but some 20-minute talks will be paired up as well. The talks will be video recorded conditioned upon the speakers' agreement.