Growth-fragmentation process embedded in a planar Brownian excursion

Brownian penalisations related to excursion lengths, VII

Limiting laws, as t →∞, for Brownian motion penalised by the longest length of excursions up to t , or up to the last zero before t , or again, up to the first zero after t , are shown to exist, and are characterized. Résumé. Il est prouvé que les lois limites, lorsque t → ∞, du mouvement brownien pénalisé par la plus grande longueur des excursions jusqu’en t , ou bien jusqu’au dernier zéro ava...

Brownian Excursion Conditioned on Its Local Time

Nonintersecting Planar Brownian Motions

In this paper we construct a measure on pairs of Brownian motions starting at the same point conditioned so their paths do not intersect. The construction of this measure is a start towards the rigorous understanding of nonintersecting Brownian motions as a conformal eld. Let B 1 ; B 2 be independent Brownian motions in R 2 starting at distinct points on the unit circle. Let T j r be the rst ti...

Random Planar Lattices and Integrated SuperBrownian Excursion

In this extended abstract, a surprising connection is described between a specific brand of random lattices, namely planar quadrangulations, and Aldous’ Integrated SuperBrownian Excursion (ISE). As a consequence, the radius rn of a random quadrangulation with n faces is shown to converge, up to scaling, to the width r = R − L of the support of the one-dimensional ISE, or more precisely:

Wright’s Constants in Graph Enumeration and Brownian Excursion Area

This is a collection of various results and formulae. The main purpose is to give explicit relations between the many different similar notations and definitions that have been used by various authors. There are no new results. This is an informal note, not intended for publication. 1. Graph enumeration Let C(n, q) be the number of connected graphs with n given (labelled) vertices and q edges. ...