## Publications## PublicationsLeading corrections to the scaling function on the diagonal for the two-dimensional Ising model,PDF (467 K) Large {$N$} Expansions for the Laguerre and Jacobi {$\beta$} Ensembles from the Loop Equations,PDF (346 K) Singular Values of Products of Ginibre Random Matrices,PDF (436 K) Painlevé II in random matrix theory and related fields,PDF (300 K) On a Family of Integrals that extend the Askey-Wilson Integral,PDF (526 K) Moments of the Gaussian {$\beta$} ensembles and the large-{$N$} expansion of the densities,PDF (607 K) Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles,PDF (437 K) Construction of a Lax pair for the {$E^{(1)}_{6}$} {$q$}-Painlevé System,PDF (335 K) Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy,PDF (813 K) Asymptotic forms for hard and soft edge general β conditional gap probabilities,PDF (291 K) On the Variance of the Index for the Gaussian Unitary Ensemble,PDF (227 K) Fredholm Determinant evaluations of the Ising Model diagonal correlations and their {$\lambda$} generalisation,PDF (521 K) Connection preserving deformations and {$q$}-semi-classical orthogonal polynomials,PDF (313 K) Physical Combinatorics and Quasiparticles,PDF (533 K) Bi-orthogonal systems on the unit circle, regular semi-classical weights and the discrete Garnier equations,PDF (220 K) Bi-orthogonal systems on the unit circle, Regular Semi-Classical Weights and Integrable Systems - II,PDF (1927 K) Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model,PDF (168 K) The Distribution of the first Eigenvalue Spacing at the Hard Edge of the Laguerre Unitary Ensemble,PDF (533 K) Boundary Conditions for Scaled Random Matrix Ensembles in the Bulk of the Spectrum,PDF (248 K) Hypergeometric Solutions to the {$q$}-Painlevé Equation of Type {$(A_1 + A_1')^{(1)}$},PDF (290 K) Random Matrix Theory and the Sixth Painlevé Equation,PDF (352 K) Boundary conditions associated with the Painlevé III' and V evaluations of some random matrix averages,PDF (221 K) Bi-orthogonal Polynomials on the Unit Circle, regular semi-classical Weights and Integrable Systems,PDF (319 K) Discrete Painlevé equations for a class of {$ \rm P_{VI} $} {$\tau$}-functions given as {$ U(N) $} averages,PDF (317 K) Gap Probabilities for Double Intervals in Hermitian Random Matrix Ensembles as τ-Functions,PDF (177 K) Discrete Painlevé equations and random matrix averages,PDF (338 K) Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable Bosons,PDF (331 K) {$\tau$}-function evaluation of Gap Probabilities in Orthogonal and Symplectic Matrix Ensembles,PDF (153 K) {$\tau$}-function Table - Jardin d'Jimbo-Miwa-Okamoto,PS (51 K) Application of the {$\tau$}-function theory of Painlevé equations to random matrices: {$ \rm P_{VI} $}, the JUE, CyUE, cJUE and scaled limits,PS (534 K) New transformations for Painlevé's third transcendent,PDF (196 K) Application of the {$\tau$}-function theory of Painlevé equations to random matrices: {$ \rm P_{V} $}, {$ \rm P_{III} $}, the LUE, JUE and CUE,PDF (534 K) Application of the {$\tau$}-function theory of {$ \rm P_{IV} $}, {$ \rm P_{II} $} to the GUE,PDF (252 K) Integrability, Random Matrices and Painlevé Transcendents,PDF (173 K) Gap Probabilities for Edge Intervals in Finite Gaussian and Jacobi Unitary Matrix Ensembles,PDF (199 K) Gap probabilities in the finite and scaled Cauchy random matrix ensembles,PDF (172 K) Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle,PDF (254 K) The Lanczos Algorithm for extensive Many-Body Systems in the Thermodynamic Limit,PDF (226 K) Moment Formalisms applied to a solvable Model with a Quantum Phase Transition. I. Exponential Moment Methods,PDF (785 K) The exact realisation of the Lanczos Method for a quantum Many-Body System,PDF (163 K) The Analytic Lanczos Method,PDF (107 K) Exact Solution to the Moment Problem for the XY Chain,PDF (208 K) Two-dimensional XXZ model ground-state properties using an analytic Lanczos expansion,PDF (137 K) Accurate calculation of ground-state energies in an analytic Lanczos expansion,PDF (144 K) Plaquette expansion proof and interpretation,PDF (691 K) Analytic solution for the ground-state energy of the extensive many-body problem,PDF (102 K) Exact solution for the reflection and diffraction of atomic de Broglie waves by a travelling evanescent laser wave,PDF (305 K) van der Waals energies of cylindrical and spherical single layer systems,PDF (1630 K) Polarisation of Scalar and Spinor vacua in QED,PDF (1486 K) Scalar QED of charged bosons in uniform magnetic fields,PDF (5995 K) |