On the block counting process and the fixation line of the\n Bolthausen-Sznitman coalescent

2016/04/15 by Jonas Kukla, Kukla, Jonas, Martin Möhle +1 · 1 citation
Mathematics · Physics and Astronomy · #60F05 #60J27 #92D15 #97K60 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1604.04514

openalex publication_date 2016/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The block counting process and the fixation line of the Bolthausen-Sznitman\ncoalescent are analyzed. Spectral decompositions for their generators and\ntransition probabilities are provided leading to explicit expressions for\nfunctionals such as hitting probabilities and absorption times. It is\nfurthermore shown that the block counting process and the fixation line of the\nBolthausen-Sznitman n-coalescent, properly scaled, converge in the Skorohod\ntopology to the Mittag-Leffler process and Neveu's continuous-state branching\nprocess respectively as the sample size n tends to infinity. Strong relations\nto Siegmund duality and to Mehler semigroups and self-decomposability are\npointed out.\n

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