Large deviations for random trees

Yuri Bakhtin; Christine Heitsch

doi:10.1007/s10955-008-9540-0

Large deviations for random trees

Yuri Bakhtin, Christine Heitsch

Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1007/s10955-008-9540-0
State	Published - Aug 2008

Keywords

Gibbs distributions
Large deviations
RNA secondary structure
Random trees

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-008-9540-0

Cite this

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title = "Large deviations for random trees",

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.",

keywords = "Gibbs distributions, Large deviations, RNA secondary structure, Random trees",

author = "Yuri Bakhtin and Christine Heitsch",

note = "Funding Information: Acknowledgements The authors thank the anonymous reviewers whose comments significantly improved the paper, and the ABC Math Program in the School of Mathematics at Georgia Tech for fostering interdisciplinary research linking mathematics with the biological sciences. This research of Yuri Bakhtin is supported in part by NSF CAREER DMS-0742424. Funding Information: This research of Christine E. Heitsch is supported in part by a Career Award at the Scientific Interface (CASI) from the Burroughs Wellcome Fund (BWF) and by NIH NIGMS 1R01GM083621-01.",

year = "2008",

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doi = "10.1007/s10955-008-9540-0",

language = "English (US)",

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AU - Heitsch, Christine

N1 - Funding Information: Acknowledgements The authors thank the anonymous reviewers whose comments significantly improved the paper, and the ABC Math Program in the School of Mathematics at Georgia Tech for fostering interdisciplinary research linking mathematics with the biological sciences. This research of Yuri Bakhtin is supported in part by NSF CAREER DMS-0742424. Funding Information: This research of Christine E. Heitsch is supported in part by a Career Award at the Scientific Interface (CASI) from the Burroughs Wellcome Fund (BWF) and by NIH NIGMS 1R01GM083621-01.

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 - RNA secondary structure

KW - Random trees

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SP - 551

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3

ER -

Large deviations for random trees

Abstract

Keywords

ASJC Scopus subject areas

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