## B. Tsirelson | ## Unitary Brownian motions | ## Recent works |

"Unitary Brownian motions are linearizable."

math.PR/9806112 (also MSRI Preprint No. 1998-027).

Available online (free of charge) from e-print archive (USA):

xxx.lanl.gov/abs/math.PR/9806112/

or its Israeli mirror:

xxx.tau.ac.il/abs/math.PR/9806112/

A long (30 pages) research preprint. Bibl. 36 refs.

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.

- Introduction.
- The white noise versus black noises.
- Spectral type of a noise.
- From unitary Brownian motions to quantum stochastic processes.
- A compactness argument.
- The commutative case.
- Appendix.

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