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Oscillatory critical amplitudes in hierarchical models and the tail of the Harris random variable
hierarchical models iteration of polynomial maps oscillatory critical amplitudes Harris random variable geometry of Julia set
2012/6/27
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....
Exact two-point resistance, and the simple random on the complete graph minus $ N$ edges
Exact two-point resistance the simple random the complete graph minus Mathematical Physics
2012/6/29
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 of random unitary matrices
Extremal spacings random unitary matrices Mathematical Physics
2012/4/16
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...
On High Moments and the Spectral Norm of Large Dilute Wigner Random Matrices
random matrices Wigner ensemble dilute random matrices
2011/9/22
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...
Induced Ginibre ensemble of random matrices and quantum operations
Induced Ginibre ensemble random matrices quantum operations
2011/9/20
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...
Discrete Schrodinger operators with random alloy-type potential
multiscale analysis fractional moment method Cartan’s Theorem localization discrete alloy-type model non-monotone
2011/9/6
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...
AC spectrum for a class of random operators at small disorder
AC spectrum random operators small disorder Spectral Theory
2011/9/1
Abstract: In this paper we present a class of Anderson type operators with independent, non-stationary (non-decaying) random potentials supported on a subset of positive density in the odd-dimensional...
Semidirect Product of Groupoids, Its Representations and Random Operators
Semidirect Product of Groupoids Representations Random Operators
2011/8/31
Abstract: One of pressing problems in mathematical physics is to find a generalized Poincar\'e symmetry that could be applied to nonflat space-times. As a step in this direction we define the semidire...
A Short Course on One-Dimensional Random Schrodinger Operators
One-Dimensional Random Schrodinger Operators Spectral Theory Mathematical Physics
2011/8/26
Abstract: We discuss various approaches to localization results for one-dimensional random Schr\"odinger operators, both discrete and continuum. We focus in particular on the approach based on F\"urst...
A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field
Processes in random environments Quantum field theory Coherent states Kinetic theory of gases
2011/8/25
Abstract: The linear Boltzmann equation is derived from a microscopic quantum model of a particle interacting, in the weak coupling limit, with a translation invariant and centered Gaussian random fie...
Understanding the Random Displacement Model: From Ground-State Properties to Localization
the Random Displacement Model Ground-State Properties Localization
2011/8/23
Abstract: We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator ...
Random walks on barycentric subdivisions and the Strichartz hexacarpet
Random walks barycentric subdivisions the Strichartz hexacarpet
2011/7/29
Abstract: We investigate the relation between simple random walks on repeated barycentric subdivisions of a triangle and a self-similar fractal, Strichartz hexacarpet, which we introduce. We explore a...
Return probability for the loop-erased random walk and mean height in sandpile : a proof
Return probability the loop-erased random walk mean height Statistical Mechanics
2011/7/28
Return probability for the loop-erased random walk and mean height in sandpile : a proof.
Universality of local spectral statistics of random matrices
Random matrix Local semicircle law Tracy-Widom distribution Dyson Brownian motion
2011/7/28
Abstract: The Wigner-Gaudin-Mehta-Dyson conjecture asserts that the local eigenvalue statistics of large random matrices exhibit universal behavior depending only on the symmetry class of the matrix e...