Leonid Pastur

Encyclopedia

**Leonid Andreevich Pastur**(Russian: Леонид Андреевич Пастур, born August 21, 1937) is a mathematical physicist and theoretical physicist, known in particular for contributions to random matrix theory, the spectral theory

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 studies of linear algebra and the solutions of...

of random Schrödinger operators, statistical mechanics

Statistical mechanics

Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...

, and solid state physics (especially, the theory of disordered systems). He is a member of the National Academy of Sciences of Ukraine. Currently, he heads the Department of Theoretical Physics at the Kharkov Institute for Low Temperature Physics and Engineering.

## Work

- In random matrix theory: together with Vladimir MarchenkoVladimir MarchenkoVladimir Marchenko is a Ukrainian mathematician who specializes in mathematical physics, in particular in the analysis of the Sturm–Liouville operators. He introduced one of the approaches to the inverse problem for Sturm–Liouville operators...

, 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, he found the first rigorous proof of universality for invariant matrix ensembles. - In the spectral theorySpectral theoryIn 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 studies of linear algebra and the solutions of...

of random Schrödinger operators, he introduced the class of metrically transitive operators, and discovered several fundamental properties of this class. Together with Ilya Goldstein and Stanislav Molchanov, he established Anderson localizationAnderson localizationIn 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...

for a class of one-dimensional self-adjoint operators with random potentials; this was the first mathematically rigorous proof of Anderson localization.