The main focus of this research project is to construct, drawing on recent advances in RMT as well as on a variety of methods from quantum field theory, a comprehensive theory describing the statistical properties of the shapes of these spectral curves, and to apply this knowledge to practical problems in wireless communications and portfolio optimisation in finance.

ndarray) Second quaternion, or set of quaternions, to compare. +50 Number of open tours by a biased rook on a specific f(n)×1 board which end on a k-th cell. In effect, this is a theory about spectral curves - the lines formed by the eigenvalues as they evolve if represented as curves in the plane whose coordinates are the value of the parameter and the magnitude of the eigenvalue. Since these early beginnings RMT has found an extraordinary variety of mathematical, physical and engineering applications that, to name some, include number. theorems for L-functions, random matrix models and prediction in number theory Random multiplicative functions. Gives a new shape to an array without changing its data. Arithmetic properties of positively reduced 2×2-matrices. Parametric RMT is the extension of RMT whose subject is the study of how these eigenvalues evolve as functions of time or other parameters characterising external perturbations applied to the systems whose properties are modelled by random matrices. The theory has numerous applications ranging from quantum physics to number theory, biology, communications theory, and mathematical finance. The theory of random matrices was introduced by John Wishart (18981956) in 1928. Random Matrix Theory (RMT) is the branch of probability theory which studies the statistical properties of the eigenvalues of large matrices whose matrix elements are random numbers.

Random matrix number theory