Spectral Theory of Large Dimensional Random Matrices and Its Applications to Wireless Communications and Finance Statistics Random Matrix Theory and Its Applications

1. Introduction. 1.1. History of RMT and current development. 1.2. Applications to wireless communications. 1.3. Applications to finance statistics -- 2. Limiting spectral distributions. 2.1. Semicircular law. 2.2. Marcenko-Pastur law. 2.3. LSD of products. 2.4. Hadamard product. 2.5. Circular law -- 3. Extreme eigenvalues. 3.1. Wigner matrix. 3.2. Sample covariance matrix. 3.3. Spectrum separation. 3.4. Tracy-Widom law -- 4. Central limit theorems of linear spectral statistics. 4.1. Motivation and strategy. 4.2. CLT of LSS for Wigner matrix. 4.3. CLT of LSS for sample covariance matrices. 4.4. F matrix -- 5. Limiting behavior of eigenmatrix of sample covariance matrix. 5.1 Earlier work by Silverstein. 5.2. Further extension of Silverstein's work. 5.3. Projecting the eigenmatrix to a d-dimensional space -- 6. Wireless communications. 6.1. Introduction. 6.2. Channel models. 6.3. Channel capacity for MIMO antenna systems. 6.4. Limiting capacity of random MIMO channels. 6.5. Concluding remarks -- 7. Limiting performances of linear and iterative receivers. 7.1. Introduction. 7.2. Linear equalizers. 7.3. Limiting SINR analysis for linear receivers. 7.4. Iterative receivers. 7.5. Limiting performance of iterative receivers. 7.6. Numerical results. 7.7. Concluding remarks -- 8. Application to finance. 8.1. Portfolio and risk management. 8.2. Factor models . 8.3. Some application in finance of factor model