Leonid Pastur

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Leonid Pastur

Leonid Andriyovych Pastur ( Ukrainian Леонід Андрійович Пастур , Russian Леонид Андреевич Пастур Leonid Andreevich Pastur ; * 21st August 1937 in Winnyzja , Ukrainian SSR ) is a Ukrainian mathematical and theoretical physicists.

Pastur studied at the Polytechnic Institute in Kharkiv from 1955 to 1961 and received his doctorate in 1964 at the Institute for Low Temperature Physics of the Ukrainian Academy of Sciences in Kharkiv (today the B. Verkin Institute for Low Temperature Physics) under Vladimir Alexandrovich Martschenko . In 1975 he completed his habilitation at the institute (Soviet doctorate). From 1968 he was Senior Research Fellow and from 1985 to 1997 head of the statistical and mathematical physics department and from 1987 to 1997 deputy director of the mathematics department. From 1978 to 1994 he was also a part-time professor at the Kharkiv State University . From 1995 to 2007 he was a professor in the mathematics faculty of the University of Paris VII and has been head of the theoretical physics department there since 2003.

He is particularly concerned with the theory of random matrices and the spectral theory of Schrödinger operators in disordered media (random potential).

In 1967, in the theory of random matrices, he and Vladimir Alexandrowitsch Martschenko found the Marchenko-Pastur law of the asymptotic distribution of eigenvalues. In 1997 he and Marija Shcherbyna proved the universality of the local eigenvalue statistics of a class of unitary random matrices.

With I. Goldsheid and S. Moltschanow , he demonstrated localization in the Anderson model in one dimension in 1977 . He introduced the class of metric transitive operators in the theory of random Schrödinger operators and examined their properties.

In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley (Spectral properties of metrically transitive operators and related problems) and at the European Congress of Mathematicians in 1996. He is a member of the Ukrainian Academy of Sciences . In 2012 he became a Fellow of the American Mathematical Society . In 1991 he gave one of the plenary lectures at the International Congress on Mathematical Physics in Leipzig. In 2002 he was a Sackler Scholar in Tel Aviv.

In 1985 he received the Ukrainian State Prize in Science and Technology. From 1997 to 2003 he was on the Executive Committee of the International Association of Mathematical Physics.

He is on the editorial board of Markov Processes and Related Fields, Geometrical and Functional Analysis, the Ukrainian Mathematical Journal, and the Journal of Low Temperature Physics.

Fonts (selection)

In addition to the works cited in the footnotes:

  • Spectra of random self adjoint operators, Uspehi Mat. Nauk., Vol. 28, 1973, pp. 3-64.
  • A simple approach to the global regime of Gaussian ensembles of random matrices, Ukrainian Math. J., Volume 57, 2005, pp. 936-966
  • From random matrices to quasi-periodic Jacobi matrices via orthogonal polynomials, J. Approx. Theory, Volume 139, 2006, pp. 269-292
  • Limiting Laws of Linear Eigenvalue Statistics for Unitary Invariant Matrix Models, J. Math. Phys., Volume 47, 2006, p. 103303
  • Eigenvalue distribution of random matrices. In: Random Media 2000 (Proceedings of the Mandralin Summer School, June 2000), Interdisciplinary Center of Mathematical and Computational Modeling, Warsaw, 2007, pp. 93-206
  • with Marija Schtscherbyna : Bulk Universality and Related Properties of Hermitian Matrix Models, J. Stat. Phys., Vol. 130, 2008, pp. 205-250, Arxiv
  • with A. Lytova : On Asymptotic Behavior of Multilinear Eigenvalue Statistics of Random Matrices, J. Stat. Phys. Volume 133, 2008, pp. 871-882
  • Orthogonal polynomials, Jacobi matrices and random matrices. In: Integrable systems and random matrices, Contemporary Mathematics 458, AMS 2008, pp. 249–263,
  • with A. Lytova: Central limit theorem for linear eigenvalue statistics of random matrices with independent entries, Annals of Probability, Volume 37, 2009, pp. 1778-1840
  • with M. Shcherbina: Eigenvalue distribution of large random matrices, AMS 2011
  • with Alexander Figotin : Spectra of random and almost-periodic operators, Grundlehren der Mathematischen Wissenschaften 297, Springer 1992
  • with Alexander Figotin: Theory of disordered spin systems, Theoretical and Mathematical Physics, Volume 35, 1978, pp. 403-414

Web links

Individual evidence

  1. ↑ Leonid Pastur in Mathematics Genealogy Project (English) Template: MathGenealogyProject / Maintenance / id used. Dissertation: The Dislocation Theory of Twin Crystals (Russian).
  2. ↑ Marchenko, Pastur, Distribution of eigenvalues ​​in certain sets of random matrices, Mat. Sb. (NS). , Volume 72, 1967, pp. 507-536
  3. ↑ Pastur, M. Shcherbina: Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles, J. Statist. Phys., Vol. 86, 1997, pp. 109-147
  4. ↑ Goldsheid, Molchanov, Pastur, A pure point spectrum for the stochastic one dimensional Schrödinger equation, Funct. Analysis Applic., Vol. 11, 1977, pp. 1-10
  5. ↑ Pastur, Spectral properties of disordered systems in the one-body approximation, Comm. Math. Phys., Vol. 75, 1980, pp. 179-196
personal data
SURNAME Pastur, Leonid
ALTERNATIVE NAMES Пастур, Леонід Андрійович (Ukrainian); Pastur, Leonid Andrijowytsch (full name)
BRIEF DESCRIPTION Ukrainian mathematical physicist
DATE OF BIRTH August 21, 1937
PLACE OF BIRTH Vinnytsia , Ukrainian SSR