“Leonid Pastur”的意思、由来-开放百科全书

Work

In random matrix theory: together with Vladimir Marchenko, he discovered the Marchenko–Pastur law.^[3] Later, he devised a more general approach to study random matrices with independent entries in the global regime.^[4] Together with Mariya Shcherbina, he found the first rigorous proof of universality for invariant matrix ensembles.^[5]

In the spectral theory of random Schrödinger operators, he introduced the class of metrically transitive operators, and discovered several fundamental properties of this class.^[6] Together with Ilya Goldsheid and Stanislav Molchanov, he established Anderson localization for a class of one-dimensional self-adjoint operators with random potentials;^[7] this was the first mathematically rigorous proof of Anderson localization.^[8]

He is a member of the National Academy of Sciences of Ukraine.^[9] In 2012 he became a fellow of the American Mathematical Society.^[10]

References

1. ^{{cite journal|last=Berezanskii|first=Yu.M.|title=Leonid Andreevich Pastur (on the occasion of his seventieth birthday)|journal=Russian Math. Surveys|year=2008|volume=63|issue=1|pages=197–199|doi=10.1070/RM2008v063n01ABEH004512|display-authors=etal}}
2. ^Webpage of ILT
3. ^{{cite journal|last=Marčenko|first=V.A.|last2=Pastur|first2=L.A.|title=Distribution of eigenvalues in certain sets of random matrices|journal=Mat. Sb. (N.S.)|year=1967|volume=72|issue=114|pages=507–536}}
4. ^{{cite journal|last=Pastur|first=L.A.|title=Spectra of random selfadjoint operators|journal=Uspekhi Mat. Nauk|year=1973|volume=28|issue=1(169)|pages=3–64}}
5. ^{{cite journal|last=Pastur|first=L.|last2=Shcherbina|first2=M.|title=Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles|journal=J. Statist. Phys.|year=1997|volume=86|issue=1–2|pages=109–147|doi=10.1007/BF02180200|bibcode=1997JSP....86..109P|citeseerx=10.1.1.55.3541}}
6. ^{{cite journal|last=Pastur|first=L.A.|title=Spectral properties of disordered systems in the one-body approximation.|journal=Comm. Math. Phys.|year=1980|volume=75|issue=2|pages=179–196|url=http://projecteuclid.org/euclid.cmp/1103908097|doi=10.1007/bf01222516}}
7. ^{{cite journal|last=Golʹdšeĭd|first=I.Ya.|last2=Molčanov|first2=S.A.|last3=Pastur|first3=L.A.|title=A random homogeneous Schrödinger operator has a pure point spectrum|journal=Funkcional. Anal. I Priložen.|year=1977|volume=11|issue=1|pages=1–10|doi=10.1007/BF01135526}}
8. ^{{cite journal|last=Spencer|first=T.|title=Mathematical aspects of Anderson localization|journal=Internat. J. Modern Phys. B|year=2010|volume=24|issue=12–13|pages=1621–1639|doi=10.1142/S0217979210064538}}
9. ^List of members of the Academy of Sciences {{webarchive|url=https://web.archive.org/web/20110830212523/http://www.nas.gov.ua/members/Pages/Academicians.aspx |date=2011-08-30 }}
10. ^List of Fellows of the American Mathematical Society, retrieved 2013-05-05.

Work

Awards and honors

References