On breadth-first constructions of scaling limits of random graphs and random unicellular maps - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Random Structures and Algorithms Année : 2022

On breadth-first constructions of scaling limits of random graphs and random unicellular maps

Résumé

We give alternate constructions of (i) the scaling limit of the uniform connected graphs with given fixed surplus, and (ii) the continuum random unicellular map (CRUM) of a given genus that start with a suitably tilted Brownian continuum random tree and make `horizontal' point identifications, at random heights, using the local time measures. Consequently, this can be seen as a continuum analogue of the breadth-first construction of a finite connected graph. In particular, this yields a breadth-first construction of the scaling limit of the critical Erd\H{o}s-R\'enyi random graph which answers a question posed in [2]. As a consequence of this breadth-first construction we obtain descriptions of the radii, the distance profiles, and the two point functions of these spaces in terms of functionals of tilted Brownian excursions.

Dates et versions

hal-02412977 , version 1 (16-12-2019)

Identifiants

Citer

Grégory Miermont, Sanchayan Sen. On breadth-first constructions of scaling limits of random graphs and random unicellular maps. Random Structures and Algorithms, 2022, 61 (4), pp.803-843. ⟨10.1002/rsa.21076⟩. ⟨hal-02412977⟩
24 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More