Toufic Suidan

A model for the bus system in Cuernavaca (Mexico)

The bus system in Cuernavaca, Mexico and its connections to random matrix distributions have been the subject of an interesting recent study by M Krbalek and P Seba in [15, 16]. In this paper we introduce and analyse a microscopic model for the bus system. We show that introducing a natural repulsion does produce random matrix distributions in natural double scaling regimes. The techniques employed include non-intersecting paths, logarithmic potential theory, determinantal point processes, and asymptotic analysis of several orthogonal polynomial ensembles. In addition, we introduce a circular bus model and include various calculations of non-crossing probabilities.

Random matrix central limit theorems for nonintersecting random walks.

We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to infinity, several limiting distributions of the walks at the mid-time behave as the eigenvalues of random Hermitian matrices as the dimension of the matrices grows to infinity.

A remark on a theorem of Chatterjee and last passage percolation

In this paper we prove universality of random matrix fluctuations of the last passage time of last passage percolation (LPP) in thin rectangles. The proof is a simple corollary of a theorem of Chatterjee. This gives an alternative (and more elementary) proof of the same result in Baik and Suidan (2005 Int. Math. Res. Not. 325–37) and Bodineau and Martin (2005 Electron. Commun. Probab. 10 105–12 (electronic)) in the special case of finite third moment.