Ipsen, Jesper R.: Products of independent Gaussian random matrices. 2015
Inhalt
- Preface
- Contents
- Why products of random matrices?
- Wireless telecommunication
- Disordered spin chains
- Stability of large complex systems
- Symplectic maps and Hamiltonian mechanics
- Quantum transport in disordered wires
- QCD at non-zero chemical potential
- From random scalars to random matrices
- Products of independent random scalars
- Products of independent random matrices
- Finite products of finite size square random matrices
- Weak commutation relation for isotropic random matrices
- From rectangular to square matrices
- Gaussian random matrix ensembles
- Wishart product matrices
- Exact results for Wishart product matrices
- Asymptotic results for Wishart product matrices
- Summary, discussion and open problems
- Eigenvalues of Gaussian product matrices
- Products of complex Ginibre matrices
- Products of quaternionic Ginibre matrices
- Products of real Ginibre matrices
- Summary, discussion and open problems
- Stability and Lyapunov exponents
- Stability and Lyapunov exponents at finite matrix dimension
- Macroscopic density for large matrix dimension
- Summary, discussion and open problems
- Matrix decompositions and their Jacobians
- Higher transcendental functions
- Bibliography