Images

The simulations in this page are for this work on the high-dimensional theory for permutons.  The Schnyder wood permuton & the Brownian separable 3-permuton Simulations for two 3-dimensional permutons. Each simulation is spinning along the Z-axis (w.r.t. the notation used in our paper). The 3-dimensional permuton associated with a permutation of size 10000 sampled from the Schnyder …

High-dimensional permutons: the Schnyder wood and Brownian separable d-permutonRead More »

The images on this page are taken from this work on the scaling and local limits of random Young tableaux. The heart example Figures for the heart example. Top-left: The Young diagram considered in the heart example. Top-right: The frozen boundary curve of the corresponding liquid region. Bottom (from left to right): a uniform random tableau …

Scaling and local limits of random Young tableauxRead More »

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 »

The length of the longest increasing subsequence in a random permutation and the size of the largest homogeneous set (i.e. a clique or an independent set) in a random graph are two of the classical problems at the interface of combinatorics and probability theory, with connections to several other areas of mathematics. In this paper, …

Long increasing subsequences and large homogenous subsetsRead More »

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 …

The skew Brownian permutonRead More »

The following images were realized during the preparation of the article “Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes”. Here you can see two uniform large Baxter permutations. We showed that they converge (in the permuton sense) to the Baxter permuton, that is a random probability measure of the unit …

Baxter permutations and bipolar orientationsRead More »