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

By Igor Kortchemski. 2015

51 citations recorded by the source corpus.

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.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ebb0d2e91465a5045a7a6a38d20b4f3c348148a0