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A Brownian‐Motion Model for the Eigenvalues of a Random Matrix
A new type of Coulomb gas is defined, consisting of n point charges executing Brownian motions under the influence of their mutual electrostatic repulsions. It is proved that this gas gives an exact
Statistical Theory of the Energy Levels of Complex Systems. I
New kinds of statistical ensemble are defined, representing a mathematical idealization of the notion of ``all physical systems with equal probability.'' Three such ensembles are studied in detail,
Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent
  • W. Press, F. Dyson
  • Psychology
    Proceedings of the National Academy of Sciences
  • 21 May 2012
TLDR
It is shown that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards, but such strategies unexpectedly do exist.
Correlations between eigenvalues of a random matrix
Exact analytical expressions are found for the joint probability distribution functions ofn eigenvalues belonging to a random Hermitian matrix of orderN, wheren is any integer andN→∞. The
Phase transitions in quantum spin systems with isotropic and nonisotropic interactions
We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic
Existence of a phase-transition in a one-dimensional Ising ferromagnet
AbstractExistence of a phase-transition is proved for an infinite linear chain of spins μj=±1, with an interaction energy $$H = - \sum J(i - j)\mu _i \mu _j ,$$ whereJ(n) is positive and monotone
The S Matrix in Quantum Electrodynamics
The covariant quantum electrodynamics of Tomonaga, Schwinger, and Feynman is used as the basis for a general treatment of scattering problems involving electrons, positrons, and photons. Scattering
Fredholm determinants and inverse scattering problems
The Gel'fand-Levitan and Marchenko formalisms for solving the inverse scattering problem are applied together to a single set of scattering phase-shifts. The result is an identity relating two
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