Thermodynamic limit for large random trees

@article{Bakhtin2010ThermodynamicLF,
  title={Thermodynamic limit for large random trees},
  author={Yuri Bakhtin},
  journal={Random Structures \& Algorithms},
  year={2010},
  volume={37}
}
  • Yuri Bakhtin
  • Published 17 September 2008
  • Mathematics
  • Random Structures & Algorithms
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… 
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References

SHOWING 1-10 OF 26 REFERENCES
Large Deviations for Random Trees
TLDR
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.
Stochastic Analysis: The Continuum random tree II: an overview
1 INTRODUCTION Many different models of random trees have arisen in a variety of applied setting, and there is a large but scattered literature on exact and asymptotic results for particular models.
Large Deviations for Random Trees and the Branching of RNA Secondary Structures
TLDR
A Large Deviation Principle with explicit rate function for the distribution of vertex degrees in plane trees, a combinatorial model of RNA secondary structures is given, with substantial agreement overall.
Markov Processes: Characterization and Convergence
Introduction. 1. Operator Semigroups. 2. Stochastic Processes and Martingales. 3. Convergence of Probability Measures. 4. Generators and Markov Processes. 5. Stochastic Integral Equations. 6. Random
Diffusion processes and their sample paths
Prerequisites.- 1. The standard BRownian motion.- 1.1. The standard random walk.- 1.2. Passage times for the standard random walk.- 1.3. Hin?in's proof of the de Moivre-laplace limit theorem.- 1.4.
What Is Enumerative Combinatorics
The basic problem of enumerative combinatorics is that of counting the number of elements of a finite set. Usually are given an infinite class of finite sets S i where i ranges over some index set I
Methods of Mathematical Finance
A Brownian Motion of Financial Markets.- Contingent Claim Valuation in a Complete Market.- Single-Agent Consumption and Investment.- Equilibrium in a Complete Market.- Contingent Claims in Incomplete
2 ,
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Berlin
  • D. Prowe
  • Environmental Science
    Journal of public health, and sanitary review
  • 1855
The following is the Report of Meteorology and Epidemics in Berlin, during the winter months of January and February, 1855. January. Up to the 12th of the month, the weather was just the same as in
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