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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2006

Multicritical continuous random trees

Résumé

We introduce generalizations of Aldous' Brownian Continuous Random Tree as scaling limits for multicritical models of discrete trees. These discrete models involve trees with fine-tuned vertex-dependent weights ensuring a k-th root singularity in their generating function. The scaling limit involves continuous trees with branching points of order up to k+1. We derive explicit integral representations for the average profile of this k-th order multicritical continuous random tree, as well as for its history distributions measuring multi-point correlations. The latter distributions involve non-positive universal weights at the branching points together with fractional derivative couplings. We prove universality by rederiving the same results within a purely continuous axiomatic approach based on the resolution of a set of consistency relations for the multi-point correlations. The average profile is shown to obey a fractional differential equation whose solution involves hypergeometric functions and matches the integral formula of the discrete approach.

Dates et versions

hal-00586655 , version 1 (18-04-2011)

Identifiants

Citer

Jérémie Bouttier, Philippe Di Francesco, Emmanuel Guitter. Multicritical continuous random trees. Journal of Statistical Mechanics: Theory and Experiment, 2006, 2006 (04), pp.P04004. ⟨10.1088/1742-5468/2006/04/P04004⟩. ⟨hal-00586655⟩
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