Random matrix theory
نویسندگان
چکیده
Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else. We include the important mathematics which is a very modern development, as well as the computational software that is transforming the theory into useful practice.
منابع مشابه
APPLICATION OF THE RANDOM MATRIX THEORY ON THE CROSS-CORRELATION OF STOCK PRICES
The analysis of cross-correlations is extensively applied for understanding of interconnections in stock markets. Variety of methods are used in order to search stock cross-correlations including the Random Matrix Theory (RMT), the Principal Component Analysis (PCA) and the Hierachical Structures. In this work, we analyze cross-crrelations between price fluctuations of 20 company stocks...
متن کاملA Block-Wise random sampling approach: Compressed sensing problem
The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initiali...
متن کامل18.338J/16.394J: The Mathematics of Infinite Random Matrices Essentials of Finite Random Matrix Theory
This handout provides the essential elements needed to understand finite random matrix theory. A cursory observation should reveal that the tools for infinite random matrix theory are quite different from the tools for finite random matrix theory. Nonetheless, there are significantly more published applications that use finite random matrix theory as opposed to infinite random matrix theory. Ou...
متن کاملOn the similarity between Nakagami-m Fading distribution and the Gaussian ensembles of random matrix theory
We report the similarity between the Nakagami-m fading distribution and the three Gaussian ensembles of random matrix theory. We provide a brief review of random matrix theory and wireless fading. We show that the Nakagami-m distribution serves as mapping between the three ensembles. The statistics of the wireless fading amplitude, as modeled by Nakagami-m distribution, provide a rare example o...
متن کاملRiemann zeros and random matrix theory
In the past dozen years random matrix theory has become a useful tool for conjecturing answers to old and important questions in number theory. It was through the Riemann zeta function that the connection with random matrix theory was first made in the 1970s, and although there has also been much recent work concerning other varieties of L-functions, this article will concentrate on the zeta fu...
متن کاملFree probability theory and random multi-matrix models
We discuss certain aspects of random multi-matrix models: random matrices chosen at random according to a certain unitarily invariant Gibbs measure on the space of N × N matrices. Thanks to work of Voiculescu, Biane, Guionnet and others, free probability tools can be used to analyze the limiting behavior of such random matrix models. In addition to touching upon a connection between such random...
متن کامل