Jacopo

[18] Reconstructing SLE-decorated Liouville quantum gravity surfaces from random permutons (with Ewain Gwynne).

Preprints

Permutons constructed from a Liouville quantum gravity surface and a pair of space-filling Schramm-Loewner evolutions (SLEs) have been shown — or are conjectured — to describe the scaling limit of various natural models of random constrained permutations.  We prove that, in two distinct and natural settings, these permutons uniquely determine, modulo rotation, scaling, translation and …

[18] Reconstructing SLE-decorated Liouville quantum gravity surfaces from random permutons (with Ewain Gwynne).Read More »

Lattice Yang-Mills theory in the large N limit via random surfaces

Talks

Lattice Yang-Mills theories are important models in particle physics. They are defined on the d-dimensional lattice  using a group of matrices of dimension , and Wilson loop expectations are the fundamental observables of these theories. Recently, Cao, Park, and Sheffield showed that Wilson loop expectations can be expressed as sums over certain embedded bipartite maps of any genus. Building on this novel approach, …

Lattice Yang-Mills theory in the large N limit via random surfacesRead More »

[3] A determinantal point process approach to scaling and local limits of random Young tableaux (with Cédric Boutillier, Valentin Féray, and Pierre-Loïc Méliot). FPSAC 2024 (to appear).

Conference papers

We obtain scaling and local limit results for large random multirectangular Young tableaux via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). In particular, we find an explicit description of the limiting surface, based on solving a complex-valued polynomial equation. As a consequence, we find a simple criteria to …

[3] A determinantal point process approach to scaling and local limits of random Young tableaux (with Cédric Boutillier, Valentin Féray, and Pierre-Loïc Méliot). FPSAC 2024 (to appear).Read More »

MATH 159 – Discrete Probabilistic Methods | 2023-2024

Teaching

This is the webpage for the course of Math 159 – Discrete Probabilistic Methods. Lecture times: Tuesday and Thursday, 1:30 PM – 2:50 PM (Hewlett Teaching Center, Rm 101). Instructor: Jacopo Borga, jborga_at_stanford.edu. Office hours: Tuesday 11:00 AM-12:15 PM (Building 380, 382-Q2). Assistant: / Office hours: / Description: In this course we will cover a range of different topics …

MATH 159 – Discrete Probabilistic Methods | 2023-2024Read More »

[17] A determinantal point process approach to scaling and local limits of random Young tableaux (with Cédric Boutillier, Valentin Féray and Pierre-Loïc Méliot). To appear in Annals of Probability.

Preprints

We obtain scaling and local limit results for large random Young tableaux of fixed shape via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove:  an explicit description of the limiting surface of a uniform random Young tableau of shape , based on solving a complex-valued …

[17] A determinantal point process approach to scaling and local limits of random Young tableaux (with Cédric Boutillier, Valentin Féray and Pierre-Loïc Méliot). To appear in Annals of Probability.Read More »

Meanders, meandric permutations, and meandric systems

Images

The images on this page are taken from this work on meanders and this work on meandric systems. Meanders and meandric permutations Left: Two large uniform meanders of size 256 and 2048. Right: The plots of the two corresponding meandric permutations. These simulations are obtained using this paper‘s Markov chain Monte Carlo algorithm. Meandric systems Simulation of a uniform …

Meanders, meandric permutations, and meandric systemsRead More »