Leonid Pastur Explained

Leonid Andreevich Pastur (Ukrainian: Леонід Андрійович Пастур, Russian: Леонид Андреевич Пастур) (born 21 August 1937) is a Ukrainian mathematical physicist and theoretical physicist, known in particular for contributions to random matrix theory, the spectral theory of random Schrödinger operators, statistical mechanics, and solid state physics (especially, the theory of disordered systems).^[1] Currently, he heads the Department of Theoretical Physics at the B Verkin Institute for Low Temperature Physics and Engineering in Kharkiv.^[2]

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]

Awards and honors

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]

Notes and References

1. Berezanskii. Yu.M.. Leonid Andreevich Pastur (on the occasion of his seventieth birthday). Russian Math. Surveys. 2008. 63. 1. 197 - 199. 10.1070/RM2008v063n01ABEH004512. etal.
2. http://www.ilt.kharkov.ua/bvi/structure/depart_e/d26/d26e.html Webpage of ILT
3. Marčenko. V.A.. Pastur. L.A.. Distribution of eigenvalues in certain sets of random matrices. Mat. Sb. . New Series. 1967. 72. 114. 507 - 536.
4. Pastur. L.A.. Spectra of random selfadjoint operators. Uspekhi Mat. Nauk. 1973. 28. 1(169). 3 - 64.
5. Pastur. L.. Shcherbina. M.. Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles. J. Statist. Phys.. 1997. 86. 1–2. 109–147. 10.1007/BF02180200. 1997JSP....86..109P. 10.1.1.55.3541. 15117770.
6. Pastur. L.A.. Spectral properties of disordered systems in the one-body approximation.. Comm. Math. Phys.. 1980. 75. 2. 179 - 196. 10.1007/bf01222516. 1980CMaPh..75..179P . 120070709.
7. Golʹdšeĭd. I.Ya.. Molčanov. S.A.. Pastur. L.A.. A random homogeneous Schrödinger operator has a pure point spectrum. Funkcional. Anal. I Priložen.. 1977. 11. 1. 1 - 10. 10.1007/BF01135526. 122146088.
8. Spencer. T.. Mathematical aspects of Anderson localization. Int. J. Mod. Phys. B. 2010. 24. 12 - 13. 1621 - 1639. 10.1142/S0217979210064538. 2010IJMPB..24.1621S .
9. http://www.nas.gov.ua/members/Pages/Academicians.aspx List of members of the Academy of Sciences
10. https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society