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On the block counting process and the fixation line of the Bolthausen/Sznitman coalescent

Venerdì 5 aprile 2019, ore 12:00, aula M1.6, primo piano, edificio Matematica, Dipartimento FIM, Modena.

Relatore: Prof. Martin Möhle (University of Tübingen).

Abstract: The block counting process and the xation line of the Bolthausen-Sznitman coalescent are analyzed. It is shown that these processes, properly scaled, converge in the Skorohod topology to the Mittag-Leffler process and to Neveu's continuous-state branching process respectively as the initial state tends to innity. Strong relations to Siegmund duality, Mehler semigroups and self-decomposability are pointed out. Furthermore, spectral decompositions for the generators and transition probabilities of the block counting process and the xation line of the Bolthausen-Sznitman coalescent are provided leading to explicit expressions for functionals such as hitting probabilities and absorption times. Extensions to exchangeable coalescents are discussed. (joint work with Jonas Kukla)

Ospiti: Prof. Cristian Giardina'

[Ultimo aggiornamento: 01/04/2021 12:33:50]