Publication

Spectrum of Exponentially Weighted Covariance Matrices

2008
Reports

Abstract

The spectrum of exponentially weighted covariance matrices is studied here. We first give a formal way of obtaining the spectrum using annealed approximation frequently used in Statistical Mechanics. Using the method developed by Bai and Silverstein we obtain the result rigorously. This spectrum matches with the spectrum obtained by annealed approximation. We also show some simulation results to see how well they match with the obtained expression.

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2008
Reports

Abstract

Official source

Related concepts (32)

Statistical mechanics

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, chemistry, and neuroscience.

Microstate (statistical mechanics)

In statistical mechanics, a microstate is a specific configuration of a system that describes the precise positions and momenta of all the individual particles or components that make up the system. Each microstate has a certain probability of occurring during the course of the system's thermal fluctuations. In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density.

Quantum statistical mechanics

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system. This can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic.

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