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.