Uniqueness of locally symmetric Brownian motion on Laakso spaces

Abstract

We take the spaces introduced by Laakso in 2000 and building on the work of Barlow, Bass, Kumagai, and Teplyaev prove the existence and uniqueness of a local symmetry invariant diffusion via heat kernel estimates. This work also builds upon works of Cheeger, Barlow and Bass, as well as the author.

v2: 16 pages, improved clarity of exposition. v1: 15 pages