Francesco Cellarosi (Queen's University)

Math Club

Thursday, March 28th, 2024

Time: 5:30 p.m.  Place: Jeffery Hall, Room 118

Speaker: Francesco Cellarosi (Queen's University)

Title: Concentration of measure on the sphere

Abstract: If we pick a point uniformly at random on a unit sphere, what is the probability that we are in close to the equator?

It turns out that for high-dimensional spheres this probability is very close to 1, showing that the "surface area" is concentrated near the equator. This already counterintuitive statement turns paradoxical if we consider the fact that it must be true for every equator…

We will discuss these facts and their connection with the isoperimetric inequality.