We apply random matrix theory (RMT) to an empirically measured financial correlation matrix, C, and show that this matrix contains a large amount of noise. In order to determine the sensitivity of the spectral properties of a random matrix to noise, we simulate a set of data and add different...

We study the existence of the weak solution of the nonlinear boundary value problem −(|u′|p−2u′)′=λ|u|p−2u+g(u)−h(x)in(0,π),u(0)=u(π)=0,where p and λ are real numbers, p1, h∈Lp′(0,π)(p′=p/(p−1)) and the nonlinearity g:R→R is a continuous function of the...

The success of random matrix theory in widely different areas of physics leads to many questions e.g. (i) when and how can a system be modelled by a random matrix, (ii) what kind of random matrix should be appropriate, (iii) how to extract the physical information from the random matrix...

Recent studies indicate that the random matrix theory can play a significant role as a model for the statistical properties of a wide range of complex systems. However, so far the results were known only for a special class of random matrix ensembles. The lack of information about the...