Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 11 (2006) > Paper 7 open journal systems 


Brownian local minima, random dense countable sets and random equivalence classes

Boris Tsirelson, Tel Aviv University


Abstract
A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are `Brownian local minima' and `unordered infinite sample'. They are identically distributed. A framework for such concepts, proposed here, includes a wide class of random equivalence classes.


Full text: PDF

Pages: 162-198

Published on: March 12, 2006
Bibliography
  1. D.J. Aldous and M.T. Barlow. On countable dense random sets. Lect. Notes Math. 850 (1981), 311-327. Math. Review 83f:60076
  2. F. Camia, L.R.G. Fontes and C.M. Newman. The scaling limit geometry of near-critical 2D percolation. arXiv:cond-mat/0510740v1. Math. Review number not available.
  3. L.R.G. Fontes, M. Isopi, C.M. Newman and K. Ravishankar. The Brownian web: characterization and convergence. arXiv:math.PR/0304119v1. Math. Review number not available.
  4. P. Iglesias-Zemmour. Diffeology. (preliminary draft, July 2005, unpublished) http://www.umpa.ens-lyon.fr/~iglesias/ Math. Review number not available.
  5. I. Karatzas, S.E. Shreve. Brownian motion and stochastic calculus. (1991) Springer (second edition). Math. Review 92h:60127
  6. A.S. Kechris. New directions in descriptive set theory. The Bulletin of Symbolic Logic 5 (1999), 161--174. Math. Review 2001h:03090
  7. A.S. Kechris. Classical descriptive set theory. Graduate Texts in Math. 156 (1995) Springer. Math. Review 96e:03057
  8. H.G. Kellerer. Duality theorems for marginal problems. Z. Wahrscheinlichkeitstheorie verw. Gebiete 67 (1984) 399-432. Math. Review 86i:28010
  9. W.S. Kendall. Stationary countable dense random sets. Adv. in Appl. Probab. 32 (2000) 86-100. Math. Review 2001g:60024
  10. J.F.C. Kingman. Poisson processes. (1993) Clarendon, Oxford. Math. Review 94a:60052
  11. Y. Peres. An invitation to sample paths of Brownian motion. Lecture notes (unpublished). http://stat-www.berkeley.edu/pub/users/peres/bmall.pdf Math. Review number not available.
  12. R. Pinciroli. Countable Borel equivalence relations and quotient Borel spaces. arXiv:math.LO/0512626v1. Math. Review number not available.
  13. S.M. Srivastava. A course on Borel sets. (1998) Springer. Math. Review 99d:04002
  14. B. Tsirelson. Nonclassical stochastic flows and continuous products. Probability Surveys 1 (2004) 173--298. Math. Review 2005m:60080
  15. B. Tsirelson. Non-isomorphic product systems. In: Advances in Quantum Dynamics (eds. G. Price et al), Contemporary Mathematics 335 (2003), AMS, pp. 273--328. Math. Review 2005b:46149 (Also arXiv:math.FA/0210457v2.)
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489