04188nam 22007095 450 991030055650332120250610110233.03-319-70885-610.1007/978-3-319-70885-0(CKB)4100000001795134(DE-He213)978-3-319-70885-0(MiAaPQ)EBC5224852(PPN)223957038(MiAaPQ)EBC29095338(EXLCZ)99410000000179513420180116d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierIntroduction to Random Matrices Theory and Practice /by Giacomo Livan, Marcel Novaes, Pierpaolo Vivo1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (IX, 124 p. 10 illus. in color.) SpringerBriefs in Mathematical Physics,2197-1757 ;263-319-70883-X Includes bibliographical references at the end of each chapters.Preface -- Getting Started -- Value the eigenvalue -- Classified Material -- The fluid semicircle -- Saddle-point-of-view -- Time for a change -- Meet Vandermonde -- Resolve(nt) the semicircle -- One pager on eigenvectors -- Finite N -- Meet Andréief -- Finite N is not finished -- Classical Ensembles:Wishart-Laguerre -- Meet Marčenko and Pastur -- Replicas -- Replicas for GOE -- Born to be free.Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum. The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory). Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.SpringerBriefs in Mathematical Physics,2197-1757 ;26PhysicsProbabilitiesMathematical physicsStatistical physicsDynamicsMathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Physics.Probabilities.Mathematical physics.Statistical physics.Dynamics.Mathematical Methods in Physics.Probability Theory and Stochastic Processes.Mathematical Physics.Statistical Physics and Dynamical Systems.Complex Systems.512.9434Livan Giacomoauthttp://id.loc.gov/vocabulary/relators/aut835319Novaes Marcelauthttp://id.loc.gov/vocabulary/relators/autVivo Pierpaoloauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910300556503321Introduction to Random Matrices2537608UNINA