Brownian Motion on graph-like spaces

TL;DR

This paper constructs Brownian motion on graph-like metric spaces and demonstrates that its cover time can be bounded based solely on the total length of the space, extending classical results to more complex structures.

Contribution

It introduces a method to define Brownian motion on a broad class of graph-like spaces and establishes a length-dependent upper bound for its cover time.

Findings

Brownian motion can be constructed on graph-like spaces.

Cover time is bounded by the space's total length.

Results extend classical Brownian motion properties to new spaces.

Abstract

We construct Brownian motion on a wide class of metric spaces similar to graphs, and show that its cover time admits an upper bound depending only on the length of the space.