A statistical Gerschgorin theorem

 

With the knowledge that the moments, especially the average and variance, of the distribution of ancestors of a cellular automaton can be gotten from the powers of readily obtained matrices, attention naturally turns to the matrices themselves. Powers, not to mention other properties, are most readily obtained from the eigenvalues and eigenvectors of any matrix, especially from the eigenvalue of largest absolute value.

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• Gerschgorin's theorem
• Positive matrices
• The statistical theorem
• Examples
  • (2,1/2) automata.
  • (2,1) automata.
  • (3,1/2) automata.
• Commentary

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Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx