184 citations · 905 across the 15 of their papers we have counts for
15 papers
Punctures and p-spin curves from matrix models III. Dl type and logarithmic potential
Shinobu Hikami
The intersection numbers for p spin curves of the moduli space M(g,n) are considered for D type by a matrix model. The asymptotic behavior of the large genus g limit and large p li…
Wilson's renormalization group: a paradigmatic shift
Edouard Brezin
A personal and subjective recollection, concerning mainly Wilson's lectures delivered over the spring of 1972 at Princeton University (summary of a talk at Cornell University on No…
The intersection numbers of the p-spin curves from random matrix theory
E. Brezin, S. Hikami
The intersection numbers of p-spin curves are computed through correlation functions of Gaussian ensembles of random matrices in an external matrix source. The p-dependence of inte…
Critical interface: twisting spin glasses at
E. Brézin, S. Franz, G. Parisi
We consider identical copies of spin glasses in finite dimension coupled at the boundaries. This allows to identify the spin glass analogous of twisted boundary conditions in ferro…
Characteristic polynomials of random matrices at edge singularities
E. Brezin, S. Hikami
We have discussed earlier the correlation functions of the random variables $\det(\la-X)$ in which is a random matrix. In particular the moments of the distribution of these ra…
Level Spacing of Random Matrices in an External Source
E. Brezin, S. Hikami
In an earlier work we had considered a Gaussian ensemble of random matrices in the presence of a given external matrix source. The measure is no longer unitary invariant and the us…
Universal singularity at the closure of a gap in a random matrix theory
E. Brezin, S. Hikami
We consider a Hamiltonian , in which is a given non-random Hermitian matrix,and is an Hermitian random matrix with a Gaussian probability dist…
Oscillating density of states near zero energy for matrices made of blocks with possible application to the random flux problem
E. Brézin, S. Hikami, A. Zee
We consider random hermitian matrices made of complex blocks. The symmetries of these matrices force them to have pairs of opposite real eigenvalues, so that the average density of…
Universal relation between Green's functions in random matrix theory
Anthony Zee, Edouard Brézin
We prove that in random matrix theory there exists a universal relation between the one-point Green's function and the connected two- point Green's function given by \vfi…
Universal correlations for deterministic plus random Hamiltonians
E. Brezin, S. Hikami, A. Zee
We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic H0 and o…
Lattices of matrices (revised)
E. Brézin, A. Zee
We study a new class of matrix models, formulated on a lattice. On each site are states with random energies governed by a Gaussian random matrix Hamiltonian. The states on dif…
Correlation Functions in Disordered Systems
E. Brezin, A. Zee
{Recently, we found that the correlation between the eigenvalues of random hermitean matrices exhibits universal behavior. Here we study this universal behavior and develop a diagr…
Perturbative analysis of an n-Ising model on a random surface
Shinobu Hikami, Edouard Brézin
Two dimensional quantum gravity coupled to a conformally invariant matter field of central charge c=n/2, is represented, in a discretized version, by n independent Ising spins per…
Renormalization Group Approach to Matrix Models
Edouard Brézin, Jean Zinn-Justin
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge or not understood. It would be useful to devise an approximate scheme whic…
A naive matrix-model approach to two-dimensional quantum gravity coupled to matter of arbitrary central charge
E. Brezin, S. Hikami
In the usual matrix-model approach to random discretized two-dimensional manifolds, one introduces n Ising spins on each cell, i.e. a discrete version of 2D quantum gravity coupled…