### Abstract

We consider Gibbs distributions on finite random plane trees with bounded branching. We show that as the order of the tree grows to infinity, the distribution of any finite neighborhood of the root of the tree converges to a limit. We compute the limiting distribution explicitly and study its properties. We introduce an infinite random tree consistent with these limiting distributions and show that it satisfies a certain form of the Markov property. We also study the growth of this tree and prove several limit theorems including a diffusion approximation.

Original language | English (US) |
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Pages (from-to) | 312-331 |

Number of pages | 20 |

Journal | Random Structures and Algorithms |

Volume | 37 |

Issue number | 3 |

DOIs | |

State | Published - Oct 1 2010 |

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### Keywords

- Gibbs distribution
- Infinite volume limit
- Random trees

### ASJC Scopus subject areas

- Software
- Mathematics(all)
- Computer Graphics and Computer-Aided Design
- Applied Mathematics