On fluctuations of cycles in a finite CW complex

Abstract

We use algebraic topology to study the stochastic mo- tion of cellular cycles in a finite CW complex. Inspired by statis- tical mechanics, we introduce a homological observable called the average current. The latter measures the average flux of the prob- ability in the process. In the low temperature, adiabatic limit, we prove that the average current fractionally quantizes, in which the denominators are combinatorial invariants of the CW complex.

Added an example showing that the average current in the low temperature adiabatic limit can be non-trivial. Corrected typos