Large deviations and the Boltzmann entropy formula

Large deviations for Wigner's law and Voiculescu's non-commutative entropy

We study the spectral measure of Gaussian Wigner's matrices and prove that it satis®es a large deviation principle. We show that the good rate function which governs this principle achieves its minimum value at Wigner's semicircular law, which entails the convergence of the spectral measure to the semicircular law. As a conclusion, we give some further examples of random matrices with spectral ...

Distribution-Invariant Risk Measures, Entropy, and Large Deviations

The simulation of distributions of financial positions is an important issue for financial institutions. If risk measures are evaluated for a simulated distribution instead of the model-implied distribution, errors of risk measurements needs to be analyzed. For distribution-invariant risk measures which are continuous on compacts we employ the theory of large deviations to study the probability...

. the Boltzmann Entropy and Randomness

The Boltzmann Entropy and Randomness Tests

In the context of the dynamical systems of classical mechanics, we introduce two new notions called “algorithmic fine-grain and coarse-grain entropy”. The fine-grain algorithmic entropy is, on the one hand, a simple variant of the randomness tests of MartinLöf (and others) and is, on the other hand, a connecting link between description (Kolmogorov) complexity, Gibbs entropy and Boltzmann entro...

Large Deviations