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Mermitian Matrix Models with Nonholomorphic Potential
Hermitian matrix models with general potential are considered. We obtainVirasoro constraints for such models and show that, in the case of...
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On orthogonal and symplectic matrix ensembles
The focus of this paper is on the probability, E β (O; J ), that a set J consisting of a finite union of intervals contains no eigenvalues for the finite N ...
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A unified framework for the Kondo problem and for an impurity in a Luttinger liquid
We develop a unified theoretical framework for the anisotropic Kondo model and the boundary sine-Gordon model. They are both boundary integrable...
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Spectral and Probabilistic Aspects of Matrix Models
The paper deals with the eigenvalue statistics of n × n random Hermitian matrices as n → ∞. We consider a certain class of unitary invariant matrix...
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Asymptotics for the Fredholm determinant of the sine kernel on a union of intervals
In the bulk scaling limit of the Gaussian Unitary Ensemble of hermitian matrices the probability that an interval of length s contains no eigenvalues...
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Dual isomonodromic deformations and moment maps to loop algebras
The Hamiltonian structure of the monodromy preserving deformation equations of Jimbo et al [JMMS] is explained in terms of parameter dependent pairs...
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Fredholm determinants, differential equations and matrix models
Orthogonal polynomial random matrix models of N × N hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (ϕ( x )ψ(...
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Level spacing distributions and the Bessel kernel
Scaling models of random N×N hermitian matrices and passing to the limit N →∞ leads to integral operators whose Fredholm determinants describe the...
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Level-spacing distributions and the Airy kernel
Scaling level-spacing distribution functions in the “bulk of the spectrum” in random matrix models of N×N hermitian matrices and then going to the...
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Hamiltonian Structure of Equations Appearing in Random Matrices
The level spacing distributions in the Gaussian Unitary Ensemble, both in the “bulk of the spectrum,” given by the Fredholm determinant of the...
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Critical Phenomena of Chemisorbed Atoms and Reconstruction — Revisited
In the theory of critical phenomena of lattice models, two dimensions holds special fascination for several reasons. In this low dimensionality,...
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Critical scaling for monodromy fields
The large scale asymptotics of the correlations for a family of two dimensional lattice field theories is calculated at the critical “temperature”.
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The continuous-spin Ising model, g0∶φ4∶d field theory, and the renormalization group
We have used the method of high-temperature series expansions to investigate the critical point properties of a continuous-spin Ising model and g 0 ∶φ 4 ∶