This algebraic deformation, which is the essence of large deviations, allows us to relate results from max-plus algebra, classical algebra, and large deviation theory. Typical examples such as tandem queues or totally asymmetric exclusion processes with general statistics will be discussed. Such examples as generalized Jackson networks or symmetric exclusion processes will be discussed. Random matrix theory studies the eigenvalues of typical large matrices.
Most matrices show strikingly regular patterns.
I will explain the patterns and show how they come up in a variety of applied problems in data analysis of large data bases, telephone encryption, particle scattering and number theory. Steve Evans Eigenvalues of uniform random matrices I'll review some of the work that has been done on the eigenvalues of uniformly distributed random matrices - particularly random unitary matrices and random isometries of local fields. Despite this variety, there is a small core of algebraic results which seem to be useful in most applications. We shall visit these classical theorems in the light of fresh results. In particular, in work with Marianne Akian, we showed that a result of precision comparable to the max-plus spectral theorem holds for convex monotone homogeneous maps, and this extension makes transparent the classical theory.