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2D and 3D Matrices to Study Linear Invadosome Formation and Activity
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Published on: June 2, 2017

Disordered ensembles of random matrices.

O Bohigas1, J X de Carvalho, M P Pato

  • 1CNRS, Université Paris-Sud, UMR8626, LPTMS, Orsay Cedex, F-91405, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed
Summary
This summary is machine-generated.

Researchers generated orthogonal invariant stable Lévy ensembles by dividing Gaussian matrices with a random variable. This method also created random graph families interpolating between Erdös-Renyi and scale-free models.

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Area of Science:

  • Statistical Mechanics
  • Random Matrix Theory
  • Network Science

Background:

  • Generalized matrix ensembles and orthogonal invariant stable Lévy ensembles are advanced topics in theoretical physics and mathematics.
  • Understanding disordered systems and their properties, such as nonergodicity, is crucial for various scientific domains.

Purpose of the Study:

  • To introduce a simple generative procedure for specific matrix ensembles and Lévy ensembles.
  • To investigate the nonergodicity of these disordered ensembles.
  • To explore the application of this procedure to random graphs and analyze the resulting models.

Main Methods:

  • Generating generalized matrix ensembles by dividing Gaussian matrices by a random variable.
  • Analyzing the properties of these ensembles, focusing on nonergodicity.
  • Applying the same generative procedure to random graphs.

Main Results:

  • Demonstrated that orthogonal invariant stable Lévy ensembles can be generated through a straightforward division of Gaussian matrices by a random variable.
  • Confirmed the nonergodicity of these disordered ensembles.
  • Showcased that applying this method to random graphs yields a family of models interpolating between the Erdös-Renyi and scale-free models.

Conclusions:

  • The simple division of Gaussian matrices by a random variable provides a unified method for generating complex mathematical structures.
  • This approach offers new insights into the nonergodicity of disordered systems.
  • The findings establish a connection between random matrix theory and network science, bridging different models of graph formation.