Large Deviations for Random Trees and the Branching of RNA Secondary Structures
@article{Bakhtin2009LargeDF, title={Large Deviations for Random Trees and the Branching of RNA Secondary Structures}, author={Yuri Bakhtin and Christine E. Heitsch}, journal={Bulletin of Mathematical Biology}, year={2009}, volume={71}, pages={84-106} }
We give a Large Deviation Principle (LDP) with explicit rate function for the distribution of vertex degrees in plane trees, a combinatorial model of RNA secondary structures. We calculate the typical degree distributions based on nearest neighbor free energies, and compare our results with the branching configurations found in two sets of large RNA secondary structures. We find substantial agreement overall, with some interesting deviations which merit further study.
19 Citations
Large Deviations for Random Trees
- MathematicsJournal of statistical physics
- 2008
A Large Deviation Principle (LDP) is proved for the distribution of degrees of vertices of the tree in a large random tree under Gibbs distributions from the analysis of RNA secondary structures.
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We study plane trees as a model for RNA secondary structure, assigning energy to each tree based on the Nearest Neighbor Thermodynamic Model, and defining a corresponding Gibbs distribution on the…
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An infinite random tree consistent with Gibbs distributions on finite random plane trees with bounded branching is introduced and it is shown that it satisfies a certain form of the Markov property.
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