Multicritical continuous random trees

Simple item page
dc.creatorBouttier, J.
dc.creatorDi Francesco, P.
dc.creatorGuitter, E.
dc.date2006-03-02
dc.date.accessioned2026-07-07T07:44:43Z
dc.date.available2026-07-07T07:44:43Z
dc.descriptionWe 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.
dc.description34 pages, 12 figures, uses lanlmac, hyperbasics, epsf
dc.identifierhttps://arxiv.org/abs/math-ph/0603007
dc.identifierhttp://arxiv.org/abs/math-ph/0603007
dc.identifierJ. Stat. Mech. (2006) P04004
dc.identifierdoi:10.1088/1742-5468/2006/04/P04004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123299
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectCombinatorics
dc.subjectProbability
dc.titleMulticritical continuous random trees
dc.typetext

Files

Collections

arXiv