Work

Multicritical continuous random trees

Year: 2006

Type: article

Abstract: We introduce generalizations of Aldous's 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.

Source: Journal of Statistical Mechanics Theory and Experiment

DOI: 10.1088/1742-5468/2006/04/p04004

Authors: J Bouttier, P Di Francesco, E Guitter

Institutions: Centre National de la Recherche Scientifique, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, CEA Paris-Saclay, Institut de Physique Théorique, University of Amsterdam

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Agence Nationale de la Recherche

Award: G766923599