### Abstract

We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.

Original language | English (US) |
---|---|

Pages (from-to) | 551-560 |

Number of pages | 10 |

Journal | Journal of Statistical Physics |

Volume | 132 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2008 |

### Fingerprint

### Keywords

- Gibbs distributions
- Large deviations
- Random trees
- RNA secondary structure

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Statistical Physics*,

*132*(3), 551-560. https://doi.org/10.1007/s10955-008-9540-0

**Large deviations for random trees.** / Bakhtin, Yuri; Heitsch, Christine.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 132, no. 3, pp. 551-560. https://doi.org/10.1007/s10955-008-9540-0

}

TY - JOUR

T1 - Large deviations for random trees

AU - Bakhtin, Yuri

AU - Heitsch, Christine

PY - 2008/8

Y1 - 2008/8

N2 - We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.

AB - We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.

KW - Gibbs distributions

KW - Large deviations

KW - Random trees

KW - RNA secondary structure

UR - http://www.scopus.com/inward/record.url?scp=46249127314&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46249127314&partnerID=8YFLogxK

U2 - 10.1007/s10955-008-9540-0

DO - 10.1007/s10955-008-9540-0

M3 - Article

AN - SCOPUS:46249127314

VL - 132

SP - 551

EP - 560

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3

ER -