![Pastur_leonid](https://upload.wikimedia.org/wikipedia/commons/5/51/Pastur_leonid.jpg)
Leonid Andreevich Pastur ( uk, Леонід Андрійович Пастур, russian: Леонид Андреевич Пастур) (born 21 August 1937) is a
Ukrainian
Ukrainian may refer to:
* Something of, from, or related to Ukraine
* Something relating to Ukrainians, an East Slavic people from Eastern Europe
* Something relating to demographics of Ukraine in terms of demography and population of Ukraine
* So ...
mathematical physicist
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...
and
theoretical physicist
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimen ...
, known in particular for contributions to
random matrix theory
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathemat ...
, the
spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result ...
of random
Schrödinger operators,
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
, and
solid state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the l ...
(especially, the theory of
disordered systems).
Currently, he heads the Department of Theoretical Physics at the
.
Work
* In
random matrix theory
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathemat ...
: together with
Vladimir Marchenko
Vladimir Alexandrovich Marchenko (russian: Влади́мир Алекса́ндрович Ма́рченко, uk, Володи́мир Олекса́ндрович Ма́рченко; born 7 July 1922) is a Soviet and Ukrainian mathematician who ...
, he discovered the
Marchenko–Pastur law. Later, he devised a more general approach to study random matrices with independent entries in the
global regime. Together with
Mariya Shcherbina
Mariya Vladimirovna Shcherbina ( uk, Марія Володимирівна Щербина, born December 11, 1958) is a Ukrainian mathematician and mathematical physicist who studies the theory of random matrices. She is a corresponding member of ...
, he found the first rigorous proof of universality for invariant matrix ensembles.
* In the
spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result ...
of random
Schrödinger operators, he introduced the class of
metrically transitive operators, and discovered several fundamental properties of this class. Together with
Ilya Goldsheid and
Stanislav Molchanov, he established
Anderson localization
In condensed matter physics, Anderson localization (also known as strong localization) is the absence of diffusion of waves in a ''disordered'' medium. This phenomenon is named after the American physicist P. W. Anderson, who was the first to sug ...
for a class of one-dimensional self-adjoint operators with random potentials; this was the first mathematically rigorous proof of Anderson localization.
Awards and honors
He is a member of the
National Academy of Sciences of Ukraine
The National Academy of Sciences of Ukraine (NASU; uk, Національна академія наук України, ''Natsional’na akademiya nauk Ukrayiny'', abbr: NAN Ukraine) is a self-governing state-funded organization in Ukraine th ...
. In 2012 he became a fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.
List of Fellows of the American Mathematical Society
retrieved 2013-05-05.
References
Mathematical physicists
Theoretical physicists
Members of the National Academy of Sciences of Ukraine
Fellows of the American Mathematical Society
20th-century Ukrainian mathematicians
20th-century Ukrainian physicists
1937 births
Living people
21st-century Ukrainian physicists
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