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Local Marchenko-Pastur Law at the Hard Edge of Sample Covariance Matrices
Random matrices ovariance matrices archenko-Pastur law ensity of states elocalization
2012/6/29
Let $X_N$ be a $N\times N$ matrix whose entries are i.i.d. complex random variables with mean zero and variance $\frac{1}{N}$. We study the asymptotic spectral distribution of the eigenvalues of the c...
Disordered quantum wires: microscopic origins of the DMPK theory and Ohm's law
Disordered quantum wires microscopic origins the DMPK theory Ohm's law Mathematical Physics
2012/4/23
We study the electronic transport properties of the Anderson model on a strip, modeling a quasi one-dimensional disordered quantum wire. In the literature, the standard description of such wires is vi...
Kramers' law: Validity, derivations and generalisations
Arrhenius’ law Kramers’ law metastability large deviations Wentzell Freidlin theory
2011/7/28
Abstract: Kramers' law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. We review different approaches that have been followed to ob...
A solvable model of fracture with power-law distribution of fragment sizes
solvable model power-law distribution Statistical Mechanics
2011/7/27
Abstract: The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade f...
Typical rank of coin-toss power-law random matrices over GF(2)
Typical coin-toss power-law
2010/11/18
Random linear systems over the Galois Field modulo 2 have an interest in connection with problems ranging from computational op-timization to complex networks.
We present a perturbative approach for studying inflation models with soft departures from scale free spectra of the power law model. In the perturbed power law (PPL) approach one obtains at the leadi...
Point Processes Modeling of Time Series Exhibiting Power-Law Statistics
point processes 1/fnoise stochastic differentiale quations power-law distributions
2010/4/27
We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activi...
A C*-algebraic model may be constructed for the description of asymptotic fields in quantum electrodynamics. In this model charged fields carry the asymptotic Coulomb field of associated charged parti...