ABSTRACT:
At time 0 start several independent lazy simple random walks on a finite
or infinite connected graph (for instance, start with 1 walker at each
vertex). When two walkers visit the same vertex at the same time they
are declared acquaintance. The social connectivity time is defined to
be the minimal time in which any two walkers have a path of acquaintances
between them. The main result in the finite settings (Joint work with
Itai Benjamini and Gady Kozma) is poly-logarithmic bounds on the social
connectivity time (when the underlying graph is of bounded degree).
As time permits a joint work with Ben Morris, Allan Sly and Chuan Qin
in which we study the model on infinite graphs will also be discussed.
The main question studied: Is it true that a.s. any two walkers will
have a path of acquaintances between them? The answer provides a
characterization of amenability.
BIO:
Jonathan Hermon is currently a p.h.d student at UC Berkeley (statistics).
He wrote a Master’s Thesis at the Weizman Institute with Itai Benjamini
as advisor.