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hal-00672669, version 1

Even Walks and Estimates of High Moments of Large Wigner Random Matrices

Oleksiy Khorunzhiy 1, V. Vengerovsky 2

(2008-12-29)

Abstract: We revisit the problem of estimates of moments of random n-dimensional matrices of Wigner ensemble by using the approach elaborated by Ya. Sinai and A. Soshnikov and further developed by A. Ruzmaikina. Our main subject is given by the structure of closed even walks and their graphs that arise in these studies. We show that the total degree of a vertex of such a graph depends not only on the self-intersections degree of but also on the total number of all non-closed instants of self-intersections of the walk. This result is used to fill the gaps of earlier considerations.

  • 1:  Laboratoire de Mathématiques de Versailles (LM-Versailles)
  • CNRS : UMR8100 – Université de Versailles Saint-Quentin-en-Yvelines
  • 2:  Mathematical Division
  • B. Verkin Institute for Low Temperature Physics
  • Domain : Mathematics/Probability
    Physics/Mathematical Physics
    Mathematics/Mathematical Physics
  • Comment : 50 pages – 4 figures. The final version – corrected – improved and detalized proofs – appendix added
 
  • hal-00672669, version 1
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  • From: Nadège Arnaud <>
  • Submitted on: Tuesday, 21 February 2012 16:52:22
  • Updated on: Thursday, 23 February 2012 09:51:48