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Semicircular Law for Hadamard Products

  • Zhidong Bai
  • Jack W. Silverstein
Chapter
Part of the Springer Series in Statistics book series (SSS)

Abstract

In nuclear physics, since the particles move with very high velocity in a small range, many excited states are seldom observed in very short time instances, and over long time periods there are no excitations. More generally, if a real physical system is not of full connectivity, the random matrix describing the interactions between the particles in the system will have a large proportion of zero elements. In this case, a sparse random matrix provides a more natural and relevant description of the system. Indeed, in neural network theory, the neurons in a person’s brain are large in number and are not of full connectivity with each other. Actually, the dendrites connected with one individual neuron are of much smaller number, probably several orders of magnitude, than the total number of neurons. Sparse random matrices are adopted in modeling these partially connected systems in neural network theory.

Keywords

Random Matrix Isomorphic Class Sparse Matrix Vertical Edge Horizontal Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Mathematics and Statistics KLAS MOE Northeast Normal UniversityChangchunChina
  2. 2.Department of Statistics and Applied ProbabilityNational University of SingaporeSingaporeSingapore
  3. 3.Department of MathematicsNorth Carolina State UniversityRaleighUS

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