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Alpha-stable branching and beta-coalescents.

Birkner, Matthias, Blath, Jochen, Capaldo, Marcella, Etheridge, Alison M., Möhle, Martin, Schweinsberg, Jason, Wakolbinger, Anton (2005)

Electronic Journal of Probability [electronic only]

Alternative definitions of conditional possibilistic measures

Ivan Kramosil (1998)

Kybernetika

The aim of this paper is to survey and discuss, very briefly, some ways how to introduce, within the framework of possibilistic measures, a notion analogous to that of conditional probability measure in probability theory. The adjective “analogous” in the last sentence is to mean that the conditional possibilistic measures should play the role of a mathematical tool to actualize one’s degrees of beliefs expressed by an a priori possibilistic measure, having obtained some further information concerning...

Amenability of linear-activity automaton groups

Gideon Amir, Omer Angel, Bálint Virág (2013)

Journal of the European Mathematical Society

We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.

An algebraic approach to Pólya processes

Nicolas Pouyanne (2008)

Annales de l'I.H.P. Probabilités et statistiques

Pólya processes are natural generalizations of Pólya–Eggenberger urn models. This article presents a new approach of their asymptotic behaviour via moments, based on the spectral decomposition of a suitable finite difference transition operator on polynomial functions. Especially, it provides new results for large processes (a Pólya process is called small when 1 is a simple eigenvalue of its replacement matrix and when any other eigenvalue has a real part ≤1/2; otherwise, it is called large).

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