The heat semigroup and Brownian motion on strip complexes

We introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing "strips" along their natural boundaries according to a given graph structure. The most familiar example is the one-dimensional complex classically associated with a graph, in which the strips are simply copies of the unit interval(one setup actually allows for variable edge lenghts). A leading key example is treebolic space, a geometric object studied in a number of recent articles, which arises as the horocyclic product of a matric tree with the hyperbolic plane.......