Unitary Brownian motions are linearizable

1998/06/19 by Boris Tsirelson, Tsirelson, Boris
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.math/9806112

arxiv created 1998/06/19 · arxiv updated 2009/11/30

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.

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