UPPER AND LOWER BOUNDS TO EIGENVALUES BY THE PARTITIONING TECHNIQUE

By EMILY CLARK

CONTENTS INTRODUCTION HISTORY OF RMT AND CURRENT DEVELOPMENT A BRIEF REVIEW OF RMT SPECTRAL ANALYSIS OF LARGE DIMENSIONAL RANDOM MATRICES LIMITS OF EXTREME EIGENVALUES CONVERGENCE RATE OF ESD CIRCULAR LAW CLT OF LINEAR SPECTRAL STATISTICS LIMITING DISTRIBUTIONS OF EXTREME EIGENVALUES AND SPACINGS APPLICATIONS TO WIRELESS COMMUNICATIONS APPLICATIONS TO FINANCE STATISTICS LIMITING SPECTRAL DISTRIBUTIONS SEMICIRCULAR LAW THE IID CASE INDEPENDENT BUT NOT IDENTICALLY DISTRIBUTED MAR?CENKO-PASTUR LAW MP LAW FOR IID CASE GENERALIZATION TO THE NON-IID CASE PROOF OF THEOREM 2 11 BY STIELTJES TRANSFORM LSD OF PRODUCTS EXISTENCE OF THE ESD OF SNTN TRUNCATION OF THE ESD OF TN TRUNCATION, CENTRALIZATION AND RESCALING OF THE X-VARIABLES SKETCH OF THE PROOF OF THEOREM 2 12 LSD OF F MATRIX SKETCH OF THE PROOF OF THEOREM 2 14 WHEN T IS A WIGNER MATRIX HADAMARD PRODUCT TRUNCATION AND CENTRALIZATION OUTLINES OF PROOF OF THE THEOREM FAILURE OF TECHNIQUES DEALING WITH HERMITIAN MATRICES REVISIT OF STIELTJES TRANSFORMATION A PARTIAL ANSWER TO THE CIRCULAR LAW COMMENTS AND EXTENSIONS OF THEOREM 2 33 EXTREME EIGENVALUES WIGNER MATRIX SAMPLE COVARIANCE MATRIX SPECTRAL RADIUS SPECTRUM SEPARATION TRACY-WIDOM LAW TW LAW FOR WIGNER MATRIX TW LAW FOR SAMPLE COVARIANCE MATRIX CENTRAL LIMIT THEOREMS OF LINEAR SPECTRAL STATISTICS MOTIVATION AND STRATEGY CLT OF LSS FOR WIGNER MATRIX OUTLINES OF THE PROOF CLT OF LSS FOR SAMPLE COVARIANCE MATRICES F MATRIX DECOMPOSITION OF XNF LIMITING DISTRIBUTION OF X† NF THE LIMITING DISTRIBUTION OF XNF LIMITING BEHAVIOR OF EIGENMATRIX OF SAMPLE COVARIANCE MATRIX EARLIER WORK BY SILVERSTEIN FURTHER EXTENSION OF SILVERSTEIN’S WORK PROJECTING THE EIGENMATRIX TO A D-DIMENSIONAL SPACE MAIN RESULTS SKETCH OF PROOF OF THEOREM 5 19 PROOF OF COROLLARY 5 23 WIRELESS COMMUNICATIONS CHANNEL MODELS BASICS OF WIRELESS COMMUNICATION SYSTEMS MATRIX CHANNEL MODELS RANDOM MATRIX CHANNELS LINEARLY PRECODED SYSTEMS CHANNEL CAPACITY FOR MIMO ANTENNA SYSTEMS SINGLE-INPUT SINGLE-OUTPUT CHANNELS MIMO FADING CHANNELS LIMITING CAPACITY OF RANDOM MIMO CHANNELS CSI-UNKNOWN CASE CSI-KNOWN CASE CONCLUDING REMARKS LIMITING PERFORMANCES OF LINEAR AND ITERATIVE RECEIVERS LINEAR EQUALIZERS ZF EQUALIZER MATCHED FILTER (MF) EQUALIZER MMSE EQUALIZER SUBOPTIMAL MMSE EQUALIZER LIMITING SINR ANALYSIS FOR LINEAR RECEIVERS ASYMPTOTIC SINR DISTRIBUTION ITERATIVE RECEIVERS MMSE-SIC BI-GDFE LIMITING PERFORMANCE OF ITERATIVE RECEIVERS MMSE-SIC RECEIVER BI-GDFE RECEIVER NUMERICAL RESULTS APPLICATION TO FINANCE PORTFOLIO AND RISK MANAGEMENT MARKOWITZ’S PORTFOLIO SELECTION FINANCIAL CORRELATIONS AND INFORMATION EXTRACTING FACTOR MODELS FROM PCA TO GENERALIZED DYNAMIC FACTOR MODELS CAPM AND APT DETERMINE THE NUMBER OF FACTORS SOME APPLICATION IN FINANCE OF FACTOR MODEL IN?ATION FORECASTING LEADING AND COINCIDENT INDEX FINANCIAL CRISES WARNING REFERENCES