Book ChapterDOI
Free Random Variables
Oliver Johnson
- pp 153-169
About:
The article was published on 2004-07-01. It has received 370 citations till now. The article focuses on the topics: Sum of normally distributed random variables & Standard normal deviate.read more
Citations
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Lectures on the Combinatorics of Free Probability
Alexandru Nica,Roland Speicher +1 more
TL;DR: In this article, the authors present a case study of non-normal distribution and non-commutative joint distributions and define a set of basic combinatorics, such as non-crossing partitions, sum-of-free random variables, and products of free random variables.
Journal ArticleDOI
Random matrix theory
Alan Edelman,N. Raj Rao +1 more
TL;DR: This article is a survey specifically oriented towards the needs and interests of a numerical analyst and includes the important mathematics which is a very modern development, as well as the computational software that is transforming the theory into useful practice.
Posted Content
The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
TL;DR: In this article, the authors consider the eigenvalues and eigenvectors of finite, low-rank perturbations of random matrices and uncover a phase transition phenomenon whereby the large matrix limit of the extreme eigen values of the perturbed matrix differs from that of the original matrix if and only if the eigvalues of the matrix are above a certain critical threshold.
Journal ArticleDOI
Infinite N phase transitions in continuum Wilson loop operators
TL;DR: In this paper, the authors define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit and show that the traces of finite powers of the Wilson loop operator stay smooth under scaling.
TRACE INEQUALITIES AND QUANTUM ENTROPY: An introductory course
TL;DR: In this article, the authors give an elementary introduction to trace inequalities and related topics in analysis, with a special focus on results that are relevant to quantum statistical mechanics, and a preliminary draft prepared for participants in Entropy and the Quantum: A school on analytic and functional inequalities with applications.
References
More filters
Book
Lectures on the Combinatorics of Free Probability
Alexandru Nica,Roland Speicher +1 more
TL;DR: In this article, the authors present a case study of non-normal distribution and non-commutative joint distributions and define a set of basic combinatorics, such as non-crossing partitions, sum-of-free random variables, and products of free random variables.
Journal ArticleDOI
Random matrix theory
Alan Edelman,N. Raj Rao +1 more
TL;DR: This article is a survey specifically oriented towards the needs and interests of a numerical analyst and includes the important mathematics which is a very modern development, as well as the computational software that is transforming the theory into useful practice.
Journal ArticleDOI
The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
TL;DR: In this article, the authors consider the eigenvalues and eigenvectors of finite, low-rank perturbations of random matrices and uncover a phase transition phenomenon whereby the large matrix limit of the extreme eigen values of the perturbed matrix differs from that of the original matrix if and only if the eigvalues of the matrix are above a certain critical threshold.
Journal ArticleDOI
Infinite N phase transitions in continuum Wilson loop operators
TL;DR: In this paper, the authors define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit and show that the traces of finite powers of the Wilson loop operator stay smooth under scaling.
TRACE INEQUALITIES AND QUANTUM ENTROPY: An introductory course
TL;DR: In this article, the authors give an elementary introduction to trace inequalities and related topics in analysis, with a special focus on results that are relevant to quantum statistical mechanics, and a preliminary draft prepared for participants in Entropy and the Quantum: A school on analytic and functional inequalities with applications.