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.
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Bakhtin, Y., Heitsch, C. Large Deviations for Random Trees. J Stat Phys 132, 551–560 (2008). https://doi.org/10.1007/s10955-008-9540-0
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DOI: https://doi.org/10.1007/s10955-008-9540-0