2009/04/09 by J. Berestycki, Berestycki, J., N. Berestycki +1
Mathematics · #60G15 #60J25 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G15 #msc:60J25
paper · pdf · doi:10.48550/arxiv.0904.1526
arxiv created 2009/04/09 · arxiv updated 2009/12/01
We describe a simple construction of Kingman's coalescent in terms of a Brownian excursion. This construction is closely related to, and sheds some new light on, earlier work by Aldous and Warren. Our approach also yields some new results: for instance, we obtain the full multifractal spectrum of Kingman's coalescent. This complements earlier work on Beta-coalescents by the authors and Schweinsberg. Surprisingly, the thick part of the spectrum is not obtained by taking the limit as α→ 2 in the result for Beta-coalescents mentioned above. Other analogies and differences between the case of Beta-coalescents and Kingman's coalescent are discussed.