Persistence of spectral projections for stochastic operators on large tensor products
Mathematical Physics
2022-04-14 v1 math.MP
Abstract
In this paper it is proved that for families of stochastic operators on a countable tensor product, depending smoothly on parameters, any spectral projection persists smoothly, where smoothness is defined using norms based on ideas of Dobrushin. A rigorous perturbation theory for families of stochastic operators with spectral gap is thereby created. It is illustrated by deriving an effective slow 2-state dynamics for a 3-state probabilistic cellular automaton. Some further potential applications are discussed.
Cite
@article{arxiv.2204.06419,
title = {Persistence of spectral projections for stochastic operators on large tensor products},
author = {Robert S MacKay},
journal= {arXiv preprint arXiv:2204.06419},
year = {2022}
}