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

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.

40 pages. Supersedes math.PR/0508414 and math.PR/0511011

References in corpus (3)

• The Brownian web: Characterization and convergence
• The Scaling Limit Geometry of Near-Critical 2D Percolation
• Countable Borel equivalence relations and quotient Borel spaces