Ensembles of random matrices and applications to Brownian bridges, Laplacian growth

We discuss a connection between ensembles of random matrices, in particularly the limiting distributions of their eigenvalues, with applications to diffusion models. Firstly we touch Brownian bridges (related with the Gaussian Unitary Ensembles with External Sources) and their application to machine learning diffusion models. Then we switch to the Normal Matrices Ensembles, which complex valued eigenvalues perform a model of the Laplacian Growth in 2-D hydrodynamics and Diffusion limited aggregation (when size of matrices tends to infinity). The main tool in our analysis is asymptotic theory for orthogonal and multiple oprthogonal polynomials.