Thermodynamic limit for large random trees

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Thermodynamic limit for large random trees
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.
Yuri Bakhtin
Added 21 May 2011
Updated 21 May 2011
Type Journal
Year 2010
Where RSA
Authors Yuri Bakhtin
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