Unitary Brownian motions are linearizable

TL;DR

This paper demonstrates that infinite-dimensional unitary Brownian motions can be represented as collections of independent one-dimensional Brownian motions, using advanced mathematical tools like tensor products and quantum measurements.

Contribution

It introduces a linearization technique for infinite-dimensional unitary Brownian motions under strong continuity, linking them to simpler one-dimensional processes.

Findings

Unitary Brownian motions are describable via countable independent Brownian motions.

Brownian motion in a separable F-space is Gaussian.

The proof employs continuous tensor products and quantum measurement theory.

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.