# 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 $$\mu_{\rho,q}$$ for different values of the parameters $$\rho\in(-1,1]$$ and $$q\in[0,1]$$.

In every row there are five simulations of $$\mu_{\rho,q}$$ and at the end there is the corresponding two-dimensional Brownian excursion of correlation $$\rho$$ in the non-negative quadrant (the specific value of $$\rho$$  is indicated at the beginning of every row). In each row, moving from left to right,  there are increasing values for the parameter $$q$$ (roughly $$q\approx 0.1,0.4,0.5,0.6,0.9$$ ).

We highlight that permutons in the same row are driven by the same Brownian excursion plotted at the end of the row and so they are coupled. Note that when $$\rho=1$$  (this is the case of the last row) the corresponding two-dimensional Brownian excursion is simply a one-dimensional Brownian excursion and it is plotted using the standard diagram for real-valued functions.

##### $$\rho=1$$

Here $$q= 1/2$$ and $$\rho=$$-0.999999999,-0.9999999,-0.99999, -0.99994,-0.9999,-0.9994,-0.999,-0.994,-0.99,-0.98,-0.97,-0.96,-0.95-0.94,-0.92,-0.91,-0.9,-0.8,-0.7,-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,0.995,0.99999