On fluctuations of cycles in a finite CW complex
Algebraic Topology
2018-07-03 v2 Dynamical Systems
Probability
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.
Keywords
Cite
@article{arxiv.1710.07995,
title = {On fluctuations of cycles in a finite CW complex},
author = {Michael J. Catanzaro and Vladimir Y. Chernyak and John R. Klein},
journal= {arXiv preprint arXiv:1710.07995},
year = {2018}
}
Comments
Added an example showing that the average current in the low temperature adiabatic limit can be non-trivial. Corrected typos