Craig A. Tracy, Harold Widom (2005)
Annales de l’institut Fourier
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We derive the limiting matrix kernels for the Gaussian orthogonal and symplectic ensembles scaled at the edge, with proofs of convergence in the operator norms that ensure convergence of the determinants.
Pavel M. Bleher, Alexander Its (2005)
Annales de l’institut Fourier
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We prove a number of results concerning the large asymptotics of the free energy of a random matrix model with a polynomial potential. Our approach is based on a deformation of potential and on the use of the underlying integrable structures of the matrix model. The main results include the existence of a full asymptotic expansion in even powers of of the recurrence coefficients of the related orthogonal polynomials for a one-cut regular potential and the double scaling asymptotics...
Soren Fournais (2002)
Annales de l’institut Fourier
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We prove a formula for the current in an electron gas in a semiclassical limit corresponding to strong, constant, magnetic fields. Little regularity is assumed for the scalar potential . In particular, the result can be applied to the mean field from magnetic Thomas-Fermi theory . The proof is based on an estimate on the density of states in the second Landau band.
Mark Pollicott, Richard Sharp (2001)
Annales de l’institut Fourier
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In this paper we study dynamical properties of linear actions by free groups via the induced action on projective space. This point of view allows us to introduce techniques from Thermodynamic Formalism. In particular, we obtain estimates on the growth of orbits and their limiting distribution on projective space.