01.06.2026 17:00 Dieter Mitsche :
On the mixing time of random geometric graphsBC1 2.01.10 (8101.02.110) (Parkring 11, 85748 Garching-Hochbrück)
We study the mixing time of the simple random walk on the giant component of supercritical $d$-dimensional random geometric graphs generated by the unit intensity Poisson Point Process in a $d$-dimensional cube of volume $n$. With $r_g$ denoting the threshold for having a giant component, we show that for every $\epsilon>0$ and any $r\geq(1+\epsilon)r_g$, the mixing time of the giant component is with high probability $\Theta(n^{2/d}/r^2)$, thereby closing a gap in the literature. Our analysis also implies that the relaxation time is of the same order. Joint work with M. Kiwi and C. Martinez.