Unitary Brownian motions are linearizable
Probability
2007-05-23 v1
Abstract
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent one-dimensional Brownian motions. The proof involves continuous tensor products and continuous quantum measurements. A by-product: a Brownian motion in a separable F-space (not locally convex) is a Gaussian process.
Cite
@article{arxiv.math/9806112,
title = {Unitary Brownian motions are linearizable},
author = {Boris Tsirelson},
journal= {arXiv preprint arXiv:math/9806112},
year = {2007}
}