Random matrix theory and applications
A rigorous analysis of disordered systems represents an open problem in statistical physics and condensed matter. To tackle the staggering complexity of such systems, one usually assumes the model parameters to be sampled from random distributions. Random Matrix Theory has wide-ranging applicability going across the analysis of the level spacing distribution in atomic nuclei, quantum chaos, evolutionary game theory, finance, and beyond.
In these lectures, I will provide useful analytical tools typically employed in the derivation of statistical properties of the eigenvalues of various classes of random matrices. I will start from a characterization of matrix models with real spectrum and discuss in particular:
- M. L. Metha, Random Matrices, Academic Press (1991).
- G. Livan, M. Novaes, P. Vivo, Introduction to random matrices: theory and practice, Springer (2018).
- M. Potters, J.-P. Bouchaud, “A First Course in Random Matrix Theory, Cambridge University Press (2020).
(Université de Paris)
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