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Universality of the Distribution Functions of Random Matrix Theory. II
This paper is a brief review of recent developments in random matrix theory.
Two aspects are emphasized: the underlying role of integrable systems and the
occurrence of the distribution functions of random matrix theory in diverse
areas of mathematics and physics.Comment: 17 pages, 3 figure
Fundamental cosmic strings
Cosmic strings are linear concentrations of energy that may be formed at
phase transitions in the very early universe. At one time they were thought to
provide a possible origin for the density inhomogeneities from which galaxies
eventually develop, though this idea has been ruled out, primarily by
observations of the cosmic microwave background (CMB). Fundamental strings are
the supposed building blocks of all matter in superstring theory or its modern
version, M-theory. These two concepts were originally very far apart, but
recent developments have brought them closer. The `brane-world' scenario in
particular suggests the existence of macroscopic fundamental strings that could
well play a role very similar to that of cosmic strings.
In this paper, we outline these new developments, and also analyze recent
observational evidence, and prospects for the future.Comment: Review to appear in Contemporary Physic
Krein systems
In the present paper we extend results of M.G. Krein associated to the
spectral problem for Krein systems to systems with matrix valued accelerants
with a possible jump discontinuity at the origin. Explicit formulas for the
accelerant are given in terms of the matrizant of the system in question.
Recent developments in the theory of continuous analogs of the resultant
operator play an essential role
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