William Da Silva

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math.PR2025

The self-dual point of Fortuin--Kasteleyn planar maps is critical

Nathanaël Berestycki, William Da Silva

We study the Fortuin--Kasteleyn model of planar maps with parameter $q \in (0, 4)$ at and away from its self-dual point. This model is also bijectively equivalent to the fully packed…

math.PR2025

Scaling limits of critical FK-decorated random planar maps with $q = 4$

William Da Silva, Xingjian Hu, Ellen Powell +1

We establish the first scaling limit for FK( $q$ )-weighted planar maps in the critical case $q = 4$ , resolving a problem that has remained open since Sheffield's seminal work arXiv:11…

math.PR2020

Growth-fragmentation process embedded in a planar Brownian excursion

E. Aïdékon, W. Da Silva

The aim of this paper is to present a self-similar growth-fragmentation process linked to a Brownian excursion in the upper half-plane $H$ , obtained by cutting the excursi…

The self-dual point of Fortuin--Kasteleyn planar maps is critical

Scaling limits of critical FK-decorated random planar maps with q=4

Growth-fragmentation process embedded in a planar Brownian excursion

Scaling limits of critical FK-decorated random planar maps with $q = 4$