1,477 research outputs found
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
What is good mathematics?
Some personal thoughts and opinions on what ``good quality mathematics'' is,
and whether one should try to define this term rigorously. As a case study, the
story of Szemer\'edi's theorem is presented.Comment: 12 pages, no figures. To appear, Bull. Amer. Math. So
Transfer operators for coupled analytic maps
We consider analytically coupled circle maps (uniformly expanding and analytic) on the -lattice with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures whose finite-dimensional marginals have analytic, exponentially bounded densities. Using residue calculus and âcluster expansionâ-like techniques we define transfer operators on these Banach spaces. We get a unique (in the considered Banach spaces) probability measure that exhibits exponential decay of correlations
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