Applications of random matrix theory to qunatum information theory and operators algebras

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Matrices are mathematical data arranged in an array. They are at the heart of mathematics and in particular, of linear algebra. They are used in almost every scientific areas. Eigenvalues is one of the important characteristics of square matrices. Random Matrix Theory (RMT) addresses the question of the typical behavior of eigenvalues of matrices whose entries are taken at random and are of large dimension. RMT has ramifications in combinatorics, operator algebras (and in particular, free probability), algebraic geometry and theoretical physics. Originally RMT was introduced by Wigner (resp. Wishart) for atomic physics (resp. statistical) purposes. Nowadays RMT research is coming back to its source with many new applications in physics and statistics.