We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called μ-random permutations. We also introduce and study a new general class of models of random permutations, called Gibbs permutation models, which combines and generalizes μ-random permutations and the celebrated Mallows model for …
The Baxter permuton is a random probability measure on the unit square which describes the scaling limit of uniform Baxter permutations. We find an explict formula for the expectation of the Baxter permuton, i.e. the density of its intensity measure. This answers a question of Dokos and Pak (2014). We also prove that all pattern …
[12] Baxter permuton and Liouville quantum gravity (with Nina Holden, Xin Sun, and Pu Yu)Read More »
This is the webpage for the course of Math 159 – Discrete Probabilistic Methods. IMPORTANT NEWS: There is a 3 hours session on June 1st, 2022 to complete the remaining student’s presentations (see below for more information on student’s presentation). This is to allow all students to give their presentation before the Exam session. Lecture times: …
Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question introducing the notion of permuton. Permuton convergence has been established for several models of random permutations in various works: we give an overview of some of these …
Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question introducing the notion of permutons. Permuton convergence has been established for several models of random permutations in various works: we give an overview of some of these results, …
The skew Brownian permuton is a universal family of limiting permutons introduced in this work. Here we collect some simulations of the skew Brownian permuton for different values of the parameters and . In every row there are five simulations of and at the end there is the corresponding two-dimensional Brownian excursion of correlation in the non-negative …
We construct a new family of random permutons, called skew Brownian permuton, which describes the limits of various models of random constrained permutations. This family is parametrized by two real parameters. For a specific choice of the parameters, the skew Brownian permuton coincides with the Baxter permuton, i.e. the permuton limit of Baxter permutations. We …
We recently introduced a new universal family of permutons, depending on two parameters, called skew Brownian permuton. For some specific choices of the parameters, the skew Brownian permuton coincides with some previously studied permutons: the biased Brownian separable permuton and the Baxter permuton. The latter two permutons are degenerate cases of the skew Brownian permuton. In …
This is the webpage for the course of Math 151 – Introduction to Probability. IMPORTANT NEWS: The first 3 weeks of lectures will be ONLINE on Zoom (but not recorded!). From Week 4 on, we will return to have in-presence lectures. The office hours of the course assistant Pranav Nuti will be in-presence starting from Week …
This is the webpage for the course MATH 136 – Stochastic Processes. IMPORTANT NEWS: The first 3 weeks of lectures will be ONLINE on Zoom (but not recorded!). From Week 4 on, we will return to have in-presence lectures. The office hours of the course assistant Panagiotis Lolas will be in-presence starting from Week 4 (but online …