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Random matrices and non-commutative probability

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Random matrices and non-commutative probability/ Arup Bose.
作者:	Bose, Arup.
出版者:	Boca Raton, FL :CRC Press, : 2022.,
面頁冊數:	1 online resource.
附註:	"A Chapman & Hall book."
標題:	Random matrices. -
電子資源:	https://www.taylorfrancis.com/books/9781003144496
ISBN:	9781003144496

Random matrices and non-commutative probability
Bose, Arup.

Random matrices and non-commutative probability[electronic resource] /Arup Bose. - 1st ed. - Boca Raton, FL :CRC Press,2022. - 1 online resource.

"A Chapman & Hall book."

Includes bibliographical references and index.

This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Mbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Mbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.

ISBN: 9781003144496

Standard No.: 10.1201/9781003144496doiSubjects--Topical Terms:

678171
Random matrices.

LC Class. No.: QA196.5

Dewey Class. No.: 512.9434

Random matrices and non-commutative probability
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300 $a 1 online resource.
500 $a "A Chapman & Hall book."
504 $a Includes bibliographical references and index.
520 $a This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Mbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Mbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
588 $a Description based on print version record.
650 0 $a Random matrices. $3 678171
650 0 $a Free probability theory. $3 1173205
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