Brownian local minima and other random dense countable sets

2005/08/22 by Boris Tsirelson, Tsirelson, Boris
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.math/0508414

18 pages

arxiv created 2005/08/22 · openalex publication_date 2005/08/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compare two examples of random dense countable sets, `Brownian local minima' and `unordered uniform infinite sample'. They appear to be identically distributed. A framework for such notions is proposed. In addition, random elements of other singular spaces (especially, reals modulo rationals) are considered.

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