Description
Book SynopsisRandom matrix theory, both as an application and as a theory, has evolved rapidly over the years. This title chronicles these developments, emphasizing log-gases as a physical picture. It covers topics such as beta ensembles and Jack polynomials. It develops the application and theory of Gaussian and circular ensembles of random matrix theory.
Trade Review"Log-Gases and Random Matrices is an excellent book. It is bound to become an instant classic and the standard reference to a large body of contemporary random matrix theory. It is a well-written tour through a vast landscape. The contemporary literature is extensively referenced and incorporated in the text, and the material is presented from several perspectives. Forrester has achieved the pedagogical equivalent of Dyson's 'Threefold Way' by writing an advanced monograph appealing equally to physicists, mathematicians, and statisticians."--Steven Joel Miller and Eduardo Duenez, Mathematical Reviews
Table of Contents*FrontMatter, pg. i*Preface, pg. v*Contents, pg. xi*Chapter One. Gaussian Matrix Ensembles, pg. 1*Chapter Two. Circular Ensembles, pg. 53*Chapter Three. Laguerre And Jacobi Ensembles, pg. 85*Chapter Four. The Selberg Integral, pg. 133*Chapter Five. Correlation functions at ss = 2, pg. 186*Chapter Six. Correlation Functions At ss= 1 And 4, pg. 236*Chapter Seven. Scaled limits at ss = 1, 2 and 4, pg. 283*Chapter Eight. Eigenvalue probabilities - Painleve systems approach, pg. 328*Chapter Nine. Eigenvalue probabilities- Fredholm determinant approach, pg. 380*Chapter Ten. Lattice paths and growth models, pg. 440*Chapter Eleven. The Calogero-Sutherland model, pg. 505*Chapter Twelve. Jack polynomials, pg. 543*Chapter Thirteen. Correlations for general ss, pg. 592*Chapter Fourteen. Fluctuation formulas and universal behavior of correlations, pg. 658*Chapter Fifteen. The two-dimensional one-component plasma, pg. 701*Bibliography, pg. 765*Index, pg. 785
