E.Khan

Random Matrices, Information Theory and Physics: New Results, New Connections

Random matrix theory has found many applications in physics, statistics and engineering since its inception. In this paper we find new results and new connections between random matrices, information theory and physics. The contributions of this paper are:
1) Recursive formula to evaluate the expectation of the characteristic polynomial of Wishart matrices
2) Relationship between the uncorrelated ergodic capacity of MIMO system and Toda lattice equation
3) Relationship between the uncorrelated ergodic capacity of MIMO system and Painleve differential equation
4) It is shown that expected characteristic polynomial of random matrix with Gaussian Unitary Ensemble (GUE) satisfies KP (Kadomtsev-Petviashvili) equations. Same is true for characteristic polynomial of Wishart matrices
5) Connection between expected value of the characteristic polynomial of Wishart matrix and Toda lattice equation.