LUCAS BENIGNI

Here are a few simulations of different probabilist models ranging from Diffusion Limited Aggregation and Glauber dynamics to the Dyson vector flow.

Dyson Vector flow - Eigenvector moment flow:

This is a simulation of the multi-particle random walk followed by the moments of eigenvectors of the Dyson Brownian motion. It was introduced in this paper.

Diffusion limited aggregation:

Some simulations of DLA-like dynamics with different initial conditions or probability of aggregation. It was introduced in this paper.

Random Matrices and Gaussian Free Field:

Simulation of the centered logarithm of the characteristic polynomial of a large random matrix which converges to the GFF. You can also find a video of its contour lines.

Glauber dynamics:

Some simulations of Glauber dynamics at the critical temperature and sub-critical temperature. It was introduced in this paper.

Self-avoiding random walk :

Simulation of a self-avoiding random walk with 4800 steps using a divide and conquer scheme. It was part of a project for a Random Simulations course where we computed some rare events on SARW.

Standard random walk:

Cover of a 10,000 square torus by a standard random walk. The asymptotic order of the cover time can be found in this paper.

Boostrap Percolation:

Boostrap percolation on a square lattice of width 1000 and a infection rate of 0.07 (close to the critical rate). It was introduced in this paper.