RANDOM MATRICES AND RANDOM PARTITIONS: NORMAL CONVERGENCE: 1 (World Scientific Series on Probability Theory and Its Applications) - Hardcover

ZHONGGEN SU

Hardcover

ISBN 10: 9814612227 ISBN 13: 9789814612227

Verlag: World Scientific, 2015

Inhaltsangabe

This book is aimed at graduate students and researchers who are interested in the probability limit theory of random matrices and random partitions. It mainly consists of three parts. Part I is a brief review of classical central limit theorems for sums of independent random variables, martingale differences sequences and Markov chains, etc. These classical theorems are frequently used in the study of random matrices and random partitions. Part II concentrates on the asymptotic distribution theory of Circular Unitary Ensemble and Gaussian Unitary Ensemble, which are prototypes of random matrix theory. It turns out that the classical central limit theorems and methods are applicable in describing asymptotic distributions of various eigenvalue statistics. This is attributed to the nice algebraic structures of models. This part also studies the Circular β Ensembles and Hermitian β Ensembles. Part III is devoted to the study of random uniform and Plancherel partitions. There is a surprising similarity between random matrices and random integer partitions from the viewpoint of asymptotic distribution theory, though it is difficult to find any direct link between the two finite models. A remarkable point is the conditioning argument in each model. Through enlarging the probability space, we run into independent geometric random variables as well as determinantal point processes with discrete Bessel kernels.

This book treats only second-order normal fluctuations for primary random variables from two classes of special random models. It is written in a clear, concise and pedagogical way. It may be read as an introductory text to further study probability theory of general random matrices, random partitions and even random point processes.

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Über die Autorin bzw. den Autor

Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.

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This book is aimed at graduate students and researchers who are interested in the probability limit theory of random matrices and random partitions. It mainly consists of three parts. Part I is a brief review of classical central limit theorems for sums of independent random variables, martingale sequences and Markov chains, etc. These classical theorems are frequently used in the study of random matrices and random partitions where random matrices are well-studied in probability theory. Part II concentrates on the asymptotic distribution theory of Circular Unitary Ensemble and Gaussian Unitary Ensemble, which are prototypes of random matrix theory. It turns out that the classical central limit theorems and methods are applicable in describing asymptotic distributions of eigenvalue statistics like linear functionals of eigenvalues. This is attributed to the nice algebraic structures of models. This part also studies the Circular Ensembles and Gaussian Ensembles, which may be viewed as extensions of the Circular Unitary Ensemble and Gaussian Unitary Ensemble. Part III is devoted to the study of random uniform and Plancherel partitions. As is known, there is a surprising similarity between random matrices and random integer partitions from the viewpoint of asymptotic distribution theory, though it is difficult to find any direct link between the two finite models.

This book treats only second-order fluctuations for primary random variables from two classes of special random models. It is written in a clear, concise and pedagogical way. It may be read as an introductory text to further study probability theory of general random matrices, random partitions and even random point processes. This book is aimed at graduate students and researchers who are interested in probability limit theory of random matrices and random integer partitions.

Details zur Ausgabe

• Verlag: World Scientific
• Erscheinungsdatum: 2015
• Sprache: Englisch
• ISBN 10: 9814612227
• ISBN 13: 9789814612227
• Einband: Tapa dura
• Anzahl der Seiten: 284
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar