William da Silva

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math.PR2026

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.PR2025

The longest increasing subsequence of Brownian separable permutons

Arka Adhikari, Jacopo Borga, Thomas Budzinski +2

We establish a scaling limit result for the length $LIS (I ¨ _{n})$ of the longest increasing subsequence of a permutation $I ¨ _{n}$ of size $n$ sampled from the Brownian se…

math.PR2025

Growth-fragmentations, Brownian cone excursions and SLE(6) explorations of a quantum disc

William Da Silva, Ellen Powell, Alexander Watson

The aim of this article is to present a growth-fragmentation process naturally embedded in a Brownian excursion from boundary to apex in a cone of angle $2 I ¨ /3$ . This growth-fragme…

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

The longest increasing subsequence of Brownian separable permutons

Growth-fragmentations, Brownian cone excursions and SLE(6) explorations of a quantum disc

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