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Sub-exponential tail bounds for conditioned stable Bienaymé–Galton–Watson trees

  • Igor KortchemskiEmail author
Article

Abstract

We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaymé–Galton–Watson trees conditioned on having a large fixed size, whose offspring distribution belongs to the domain of attraction of a stable law. This extends results obtained for the height and width by Addario-Berry, Devroye and Janson in the finite variance case.

Keywords

Random trees Bienaymé–Galton–Watson trees Spectrally positive stable Lévy processes Non-crossing trees 

Mathematics Subject Classification

Primary 60J80 05C05 05C07 Secondary 60F05 60G52 

Notes

Acknowledgments

The author is grateful to Louigi Addario-Berry and to Svante Janson for stimulating discussions, as well as to an anonymous referee for her or his extremely careful reading and many comments that greatly improved the paper, and would like to thank the Newton Institute, where this work was finalized, for hospitality.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.CNRS and CMAPÉcole polytechniquePalaiseauFrance

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