Random Complexes via Topologically-Inspired Determinants

Russ Lyons, Indiana University
Fine Hall 314

Uniform spanning trees on finite graphs and their analogues on infinite graphs are a well-studied area. We present the basic elements of a higher-dimensional analogue on finite and infinite CW-complexes. On finite complexes, they relate to (co)homology, while on infinite complexes, they relate to $\ell2$-Betti numbers. One use is to get uniform isoperimetric inequalities.