Speaker : Wai Kit Lam (National Taiwan University)
Title : On the geometry of the growing ball of first-passage percolation
Time : 2022-12-02 (Fri) 14:00 - 15:00
Place : Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Abstract: In first-passage percolation, one puts i.i.d. nonnegative weights on the nearest-neighbor edges, and studies the induced (pseudo)metric. It is well-known that a metric ball of radius $t$, after rescaled by $1/t$, converges to a deterministic limit shape as $t \to \infty$. However, not too much is known for finite $t$. In this talk, we will focus on the geometry of a ball of radius $t$, by studying its boundary. We will first talk about the size of the boundary of a ball (based on an earlier joint work with M. Damron and J. Hanson), and then we will talk about holes in a ball (based on a recent joint work with M. Damron, J. Gold and X. Shen).