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 …
For large combinatorial structures, two main notions of convergence can be defined: scaling limits and local limits. In particular, for graphs both notions are well-studied and well-understood. For permutations only a notion of scaling limits, called permutons, has been investigated in the last decade. In the first part of the talk, we introduce a new …
Local limits for permutations and generating treesRead More »
We look at geometric limits of large random non-uniform permutations. We mainly consider two theories for limits of permutations: permuton limits, introduced by Hoppen, Kohayakawa, Moreira, Rath, and Sampaio to define a notion of scaling limits for permutations; and Benjamini-Schramm limits, introduced by the author to define a notion of local limits for permutations. The models of …
[Ph.D] Random Permutations: A geometric point of viewRead More »
This is the webpage for the course of Stochastik. Teacher: Ashkan Nikeghbali The lectures for this course are recorded. All the material can be found here: Stochastik 2021 – Dropbox. The live sessions (Q&A sessions and exercise classes) will be on zoom (Zoom-link). The plan is as follows: -Monady 10.15-12: Q&A session with Alejandro -Wednesday 13.00-14.45: exercise …
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 by presenting the notion of permuton convergence. Then we answer the question for different choices of random permutation models. We mainly focus on two examples of permuton convergence, introducing …