Jacopo

The skew Brownian permuton

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, …

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The skew Brownian permuton

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 …

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[11] The skew Brownian permuton: a new universality class for random constrained permutations

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 …

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[10] The permuton limit of strong-Baxter and semi-Baxter permutations is the skew Brownian permuton

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 …

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[Ph.D] Random Permutations: A geometric point of view

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 …

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Probability I 2021

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 …

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