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Random phase approximation (RPA) was proposed by Bohm and Pines in four seminal papers during 1951-1953 to describe the correlation of fermions, namely the correction to the Hartree-Fock theory. While...
Liouville quantum gravity (LQG) is a theory of random surfaces that originated from string theory. Schramm Loewner evolution (SLE) is a family of random planar curves describing scaling limits of many...
In theories in which the parameters of the low energy theory are not unique, perhaps having different values in different domains of the universe as is possible in some inflationary models, the fermio...
Abstract One way that an anthropic selection mechanism may be manifest in a physical theory involves multiple domains in the universe with different values of the physical parameters. If this mechanis...
I briefly describe two motivations, two mechanisms and two possible tests of the hypothesis that the physical parameters of the ground state of a theory can vary in different rerions of the universe.
In this paper the three-dimensional random-field Ising model is studied at both zero temperature and positive temperature. Critical exponents are extracted at zero temperature by finite size scaling a...
Oscillatory critical amplitudes have been repeatedly observed in hierarchical models and, in the cases that have been taken into consideration, these oscillations are so small to be hardly detectable....
An analytical approach is developed to obtain the exact expressions for the two-point resistance, and the total effective resistance of the complete graph minus $N$ edges of the opposite vertices. The...
Extremal spacings between unimodular eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Probability distributions for the minimal spacing for various e...
The short and intense pulses of the new X-ray free electron lasers, now operational or under construction, may make possible diffraction experiments on single molecule-sized objects with high resoluti...
Abstract: We consider a dilute version of the Wigner ensemble of n-dimensional random matrices H such that each row has in average \rho_n non-zero elements. We study asymptotic properties of the spect...
Abstract: A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matri...
Abstract: The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a K\"ahler manifold. The main idea is to use finite dimensional spaces of Bergma...
Abstract: We review recent results on localization for discrete alloy-type models based on the multiscale analysis and the fractional moment method, respectively. The discrete alloy-type model is a fa...
Abstract: We present new, original and alternative method for searching signals coded in noisy data. The method is based on the properties of random matrix eigenvalue spectra. First, we describe gener...

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