2002/04/07 by Alexandre Borovik, Alexandre V. Borovik, Alexei Myasnikov +5
Computer Science · Mathematics · #20E05 #60B15 #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Limits and Structures in Graph Theory #Probability (math.PR) #Topological and Geometric Data Analysis #math.GR #math.PR #msc:20E05 #msc:60B15
paper · pdf · doi:10.48550/arxiv.math/0204078
22 pages
arxiv created 2002/04/07 · openalex publication_date 2002/04/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a property P with probability p". The validity of a statement like that does, of course, heavily depend on how one defines probability on groups, or, equivalently, how one measures sets in a group (in particular, in a free group). We hope that new approaches to defining probabilities on groups outlined in this paper create, among other things, an appropriate framework for the study of the "average case" complexity of algorithms on groups.