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Introduction to Random Matrices = Theory and Practice /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Introduction to Random Matrices/ by Giacomo Livan, Marcel Novaes, Pierpaolo Vivo.
其他題名:	Theory and Practice /
作者:	Livan, Giacomo.
其他作者:	Novaes, Marcel.
面頁冊數:	IX, 124 p. 10 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Physics. -
電子資源:	https://doi.org/10.1007/978-3-319-70885-0
ISBN:	9783319708850

Introduction to Random Matrices = Theory and Practice /
Livan, Giacomo.

Introduction to Random MatricesTheory and Practice /[electronic resource] :by Giacomo Livan, Marcel Novaes, Pierpaolo Vivo. - 1st ed. 2018. - IX, 124 p. 10 illus. in color.online resource. - SpringerBriefs in Mathematical Physics,262197-1757 ;. - SpringerBriefs in Mathematical Physics,8.

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.

ISBN: 9783319708850

Standard No.: 10.1007/978-3-319-70885-0doiSubjects--Topical Terms:

564049
Physics.

LC Class. No.: QC5.53

Dewey Class. No.: 530.15

Introduction to Random Matrices = Theory and Practice /
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