B. Tsirelson

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

Recent works

Boris Tsirelson,
"Brownian local minima, random dense countable sets and random equivalence classes".
Electronic Journal of Probability 11:7, 162-198 (2006).
Available online (free of charge) on the journal site:
http://www.math.washington.edu/~ejpecp/EjpVol11/paper7.abs.html
See also arXiv.org/abs/math.PR/0601673/


A research paper, 37 pages, bibl. 15 refs.

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.

  1. Introduction.
  2. Main lemma.
  3. Random countable sets.
  4. Selectors.
  5. Independence.
  6. Selectors and independence.
  7. Main results.
  8. Borelogy, the new framework.
  9. Probability measures on singular spaces.
  10. Some generalizations and final remarks.
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