Jacopo

[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).

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

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.

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

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 »

Long increasing subsequences in Brownian-type permutations

What is the behavior of the longest increasing subsequence of a uniformly random permutation? Its length is of order  plus Tracy–Widom fluctuations of order . Its scaling limit is the directed geodesic of the directed landscape.  This talk discusses how this behavior changes dramatically when one looks at universal Brownian-type permutations, i.e., permutations sampled from the Brownian separable permutons. We show that there are explicit constants such that …

Long increasing subsequences in Brownian-type permutationsRead More »

[16] Power-law bounds for increasing subsequences in Brownian separable permutons and homogeneous sets in Brownian cographons (with William Da Silva and Ewain Gwynne). To appear in Advances in Mathematics.

The Brownian separable permutons are a one-parameter family – indexed by – of universal limits of random constrained permutations. We show that for each , there are explicit constants such that the length of the longest increasing subsequence in a random permutation of size sampled from the Brownian separable permuton is between and with probability …

[16] Power-law bounds for increasing subsequences in Brownian separable permutons and homogeneous sets in Brownian cographons (with William Da Silva and Ewain Gwynne). To appear in Advances in Mathematics.Read More »