RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Fundam. Prikl. Mat., 1997, Volume 3, Issue 3, Pages 903–923 (Mi fpm250)  

On eigenvalue distribution in some ensembles of large random matrices

A. Yu. Plakhov

Institute for Physico-Technical Problems

Abstract: In the paper the differential equation obtained by V. A. Marchenko and L. A. Pastur [1] is examined which describes spectral distribution in some ensembles of large random matrices. The solution of this equation is explicitly found, as well as the rule proposed in [1] for finding out intervals on real axis complement to spectrum is proven. The methods of V. A. Marchenko and L. A. Pastur are applied in the neural networks theory for studying evolution of spectrum of interneuron connection matrix describing REM sleep. Asymptotic behavior of spectrum is investigated; it is proven to differ qualitatively in cases where a parameter $\alpha$ corresponding to memory loading with memorizing patterns is less than some critical value $\alpha_c$, and where $\alpha>\alpha_c$. From viewpoint of associative memory in neural networks, all the patterns are memorized as a result of sleeping in the first case, and are not in the second one.

Full text: PDF file (857 kB)

Bibliographic databases:
UDC: 517.53/.578+518.95/.957
Received: 01.01.1996

Citation: A. Yu. Plakhov, “On eigenvalue distribution in some ensembles of large random matrices”, Fundam. Prikl. Mat., 3:3 (1997), 903–923

Citation in format AMSBIB
\Bibitem{Pla97}
\by A.~Yu.~Plakhov
\paper On eigenvalue distribution in some ensembles of large random matrices
\jour Fundam. Prikl. Mat.
\yr 1997
\vol 3
\issue 3
\pages 903--923
\mathnet{http://mi.mathnet.ru/fpm250}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1794149}
\zmath{https://zbmath.org/?q=an:0928.15014}


Linking options:
  • http://mi.mathnet.ru/eng/fpm250
  • http://mi.mathnet.ru/eng/fpm/v3/i3/p903

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Фундаментальная и прикладная математика
    Number of views:
    This page:168
    Full text:54
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020