A conditioning principle for Galton-Watson trees

Nathanael Berestycki; Peter Morters; Nadia Sidorova

A conditioning principle for Galton-Watson trees

Probability 2012-04-17 v2

Authors: Nathanael Berestycki , Peter Morters , Nadia Sidorova

Abstract

We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than $\eps$ , converges as $\eps\downarrow 0$ in law to the regular $\mu$ -ary tree, where $\mu$ is the essential minimum of the offspring distribution. This gives an example of entropic repulsion where the limit has no entropy.

Keywords

random trees

Cite

@article{arxiv.1006.2315,
  title  = {A conditioning principle for Galton-Watson trees},
  author = {Nathanael Berestycki and Peter Morters and Nadia Sidorova},
  journal= {arXiv preprint arXiv:1006.2315},
  year   = {2012}
}

Comments

This is now superseded by a new paper, arXiv:1204.3080, written jointly with Nina Gantert. The new paper contains much stronger results (e.g. the two-point concentration of the level at which the Galton-Watson tree ceases to be minimal) based on a significantly more delicate analysis, making the present paper redundant

A conditioning principle for Galton-Watson trees

Abstract

Keywords

Cite

Comments

Related papers