142 citations · 462 across the 17 of their papers we have counts for
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Lehmer's Interesting Series
F. J. Dyson, N. E. Frankel, M. L. Glasser
The series $$S_k(z)=\sum_{m=1}^{\infty}\frac{m^kz^m}{(\{array}{c} 2m m \{array})}$$ is evaluated in non-recursive closed and analytically continued beyond its domain of convergence…
Edge effects in some perturbations of the GUE
K. E. Bassler, P. J. Forrester, N. E. Frankel
A bordering of GUE matrices is considered, in which the bordered row consists of zero mean complex Gaussians N off the diagonal, and the real Gaussian N…
Eigenvalue Separation in Some Random Matrix Models
Kevin E. Bassler, Peter J. Forrester, Norman E. Frankel
The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount…
Asymptotic form of the density profile for Gaussian and Laguerre random matrix ensembles with orthogonal and symplectic symmetry
P. J. Forrester, N. E. Frankel, T. M. Garoni
In a recent study we have obtained correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random…
Asymptotic corrections to the eigenvalue density of the GUE and LUE
T. M. Garoni, P. J. Forrester, N. E. Frankel
We obtain correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N by N matrices, both in…
Applications and generalizations of Fisher-Hartwig asymptotics
P. J. Forrester, N. E. Frankel
Fisher-Hartwig asymptotics refers to the large form of a class of Toeplitz determinants with singular generating functions. This class of Toeplitz determinants occurs in the st…
Random matrix averages and the impenetrable Bose gas in Dirichlet and Neumann boundary conditions
P. J. Forrester, N. E. Frankel, T. M. Garoni
The density matrix for the impenetrable Bose gas in Dirichlet and Neumann boundary conditions can be written in terms of , wher…
On the ubiquity of the Levy integral, its relationship with the generalised Euler-Jacobi series, and their asymptotics beyond all orders
T. M. Garoni, N. E. Frankel
We present here an overview of the history, applications and important properties of a function which we refer to as the Levy integral. For certain values of its characteristic par…
Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable Bosons
P. J. Forrester, N. E. Frankel, T. M. Garoni +1
The recent experimental realisation of a one-dimensional Bose gas of ultra cold alkali atoms has renewed attention on the theoretical properties of the impenetrable Bose gas. Of pr…