Explaining Deviations from Okun's Law

Large Deviations from the Circular Law

We prove a full large deviations principle in the scale N for the empirical measure of the eigenvalues of an N N non self adjoint matrix composed of i i d zero mean random variables with variance N The good rate function which governs this rate func tion possesses as unique minimizer the circular law providing an alter native proof of convergence to the latter The techniques are related to rece...

3 Deviations from the Circular Law

Consider Ginibre's ensemble of N × N non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance 1 N. As N ↑ ∞ the normalized counting measure of the eigenvalues converges to the uniform measure on the unit disk in the complex plane. In this note we describe fluctuations about this Circular Law. First we obtain finite N formulas for the covaria...

A Quantitative Treatment of Deviations from Raoult's Law.

Deviations from uniform power law scaling in nonstationary time series.

A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor an...

Explaining Zipf's Law via Mental Lexicon

Zipf's law is the major regularity of statistical linguistics that has served as a prototype for rank-frequency relations and scaling laws in natural sciences. Here we show that Zipf's law-together with its applicability for a single text and its generalizations to high and low frequencies including hapax legomena-can be derived from assuming that the words are drawn into the text with random p...