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Titlebook: Random Matrices and Iterated Random Functions; Münster, October 201 Gerold Alsmeyer,Matthias Löwe Conference proceedings 2013 Springer-Verl

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书目名称Random Matrices and Iterated Random Functions
副标题Münster, October 201
编辑Gerold Alsmeyer,Matthias Löwe
视频video
概述Brings together two active areas of modern probability theory.Provides survey articles that are also readable for non-experts.Refereed according to journal standards.Includes supplementary material:
丛书名称Springer Proceedings in Mathematics & Statistics
图书封面Titlebook: Random Matrices and Iterated Random Functions; Münster, October 201 Gerold Alsmeyer,Matthias Löwe Conference proceedings 2013 Springer-Verl
描述​Random Matrices are one of the major research areas in modern probability theory, due to their prominence in many different fields such as nuclear physics, statistics, telecommunication, free probability, non-commutative geometry, and dynamical systems. A great deal of recent work has focused on the study of spectra of large random matrices on the one hand and on iterated random functions, especially random difference equations, on the other. However, the methods applied in these two research areas are fairly dissimilar. Motivated by the idea that tools from one area could potentially also be helpful in the other, the volume editors have selected contributions that present results and methods from random matrix theory as well as from the theory of iterated random functions. This work resulted from a workshop that was held in Münster, Germany in 2011. The aim of the workshop was to bring together researchers from two fields of probability theory: random matrix theory and the theory of iterated random functions. Random matrices play fundamental, yet very different roles in the two fields. Accordingly, leading figures and young researchers gave talks on their field of interest that w
出版日期Conference proceedings 2013
关键词60B20, 46L54, 60B15, 60F05, 60J05, 60J80, 60K05; free probability; implicit renewal theory; iterated ra
版次1
doihttps://doi.org/10.1007/978-3-642-38806-4
isbn_softcover978-3-642-43122-7
isbn_ebook978-3-642-38806-4Series ISSN 2194-1009 Series E-ISSN 2194-1017
issn_series 2194-1009
copyrightSpringer-Verlag Berlin Heidelberg 2013
The information of publication is updating

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Asymptotic Eigenvalue Distribution of Random Matrices and Free Stochastic Analysistrices. The main concrete results center around the free Fourth Moment Theorem, which says that for a sequence of random variables which are constrained to live in a fixed free chaos, the convergence to the semicircle distribution can be controlled by the convergence of the second and the fourth moments.
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Precise Tail Index of Fixed Points of the Two-Sided Smoothing Transforml mild moment condition on the .., our main result asserts that . the main contribution being that . is indeed positive and therefore . the precise tail index of | . | , for the convergence was recently shown by Jelenkovic and Olvera-Cravioto [.].
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Large Deviation Tail Estimates and Related Limit Laws for Stochastic Fixed Point Equationsxceedance probability. In the process, we establish an interesting connection between the regularity properties of {..} and the recurrence properties of an associated .-shifted Markov chain. We illustrate these ideas with several examples.
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Asymptotic Eigenvalue Distribution of Random Matrices and Free Stochastic Analysisvide us with tools for qualitative descriptions of the asymptotic eigenvalue distribution of selfadjoint polynomials of independent Gaussian random matrices. The main concrete results center around the free Fourth Moment Theorem, which says that for a sequence of random variables which are constrain
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