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Random matrix theory: Dyson Brownian motion

Snapshots of modern mathematics from Oberwolfach

Random matrix theory: Dyson Brownian motion

The theory of random matrices was introduced by John Wishart (1898–1956) in 1928. The theory was then developed within the field of nuclear physics from 1955 by Eugene Paul Wigner (1902–1995) and later by Freeman John Dyson, who were both concerned with the statistical description of heavy atoms and their electromagnetic properties. In this snap- shot, we show how mathematical properties can have unexpected links to physical phenomenena. In particular, we show that the eigenvalues of some particular random matrices can mimic the electrostatic repul- sion of the particles in a gas.

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Mathematical subjects

Algebra and Number Theory
Probability Theory and Statistics

Connections to other fields

Physics

Author(s)

Gianluca Finocchio

License

DOI (Digital Object Identifier)

10.14760/SNAP-2020-002-EN

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snapshots-2020-002.pdf

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