Random Matrix Theory (RMT) describes the statistical properties of the eigenvalue spectra of matrix ensembles with random entries. Devised in the early fifties to describe the physical properties of heavy nuclei, RMT has found more and more applications in very diverse fields, ranging from several areas of Theoretical Physics and Mathematics to Genomics and Information Theory.
In this talk I will describe the most relevant properties of random correlation matrix ensembles, and show how their benchmark statistical properties can be used to disentangle information from noise in the eigenvalue spectra of real-world correlated data. I will then review some applications of these results to the correlation analysis of financial data. In particular, I will describe the main spectral features observed in the correlation matrices of daily financial returns, and show some applications to the optimal portfolio selection problem.