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Asymptotics of the Fredholm determinant corresponding to the first bulk critical universality class in random matrix models
Integrable operators Riemann-Hilbert approach Deift-Zhou method asymptotical analysis of Fredholm determinants
2015/1/19
We study the one-parameter family of determinants $det(I-\gamma K_{PII}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{PII}$ acting on the interval $(-s,s)$ whose kernel is constructed o...
Asymptotic expansion of beta matrix models in the one-cut regime
Asymptotic expansion beta matrix models the one-cut regime Probability
2011/8/26
Abstract: We prove the existence of a 1/N expansion to all orders in beta matrix models with a confining, off-critical potential corresponding to an equilibrium measure with a connected support. Thus,...
The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, part I
largest eigenvalue of real symmetric Hermitian and Hermitian self-dual random matrix rank one external source
2011/2/22
We consider the limiting location and limiting distribution of the largest eigenvalue in real
symmetric (β = 1), Hermitian (β = 2), and Hermitian self-dual (β = 4) random matrix models
with rank 1 e...
We construct a free fermion and matrix model representation of refined BPS generating functions of D2 and D0 branes bound to a single D6 brane, in a class of toric manifolds
without compact four-cycl...
A method for constructing random matrix models of disordered bosons
random matrix models disordered bosons
2011/2/22
Random matrix models of disordered bosons consist of matrices in the Lie algebra g = spn(R). Assuming dynamical stability, their eigenvalues are required to be purely imaginary.