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Limit distributions for multitype branching processes of m -ary search trees

Brigitte Chauvin, Quansheng Liu, Nicolas Pouyanne (2014)

Annales de l'I.H.P. Probabilités et statistiques

Let m 3 be an integer. The so-called m -ary search treeis a discrete time Markov chain which is very popular in theoretical computer science, modelling famous algorithms used in searching and sorting. This random process satisfies a well-known phase transition: when m 26 , the asymptotic behavior of the process is Gaussian, but for m 27 it is no longer Gaussian and a limit W D T of a complex-valued martingale arises. In this paper, we consider the multitype branching process which is the continuous time version...

Limit shapes of Gibbs distributions on the set of integer partitions : the expansive case

Michael M. Erlihson, Boris L. Granovsky (2008)

Annales de l'I.H.P. Probabilités et statistiques

We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak∼Ckp−1, k→∞, p>0, where C is a positive constant. The measures considered are associated with the generalized Maxwell–Boltzmann models in statistical mechanics, reversible coagulation–fragmentation processes and combinatorial structures, known as assemblies. We prove a central limit theorem for fluctuations of a properly scaled partition...

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