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):
or its Israeli mirror:

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.

  1. Introduction.
  2. The white noise versus black noises.
  3. Spectral type of a noise.
  4. From unitary Brownian motions to quantum stochastic processes.
  5. A compactness argument.
  6. The commutative case.
  7. Appendix.
back to Preprints of 1999 and before back to my homepage