Transmissibility Matrix in Harmonic and Random Processes

Determinantal point processes and random matrix theory in a nutshell

3 Universality 5 3.1 Macroscopic behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Wigner’s semicircle law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Microscopic behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2.1 Bulk universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Relaxation processes in harmonic glasses?

A relaxation process, with the associated phenomenology of sound attenuation and sound velocity dispersion, is found in a simulated harmonic Lennard-Jones glass. We propose to identify this process with the so-called microscopic (or, instantaneous) relaxation process observed in real glasses and supercooled liquids. A model based on the memory function approach accounts for the observation and ...

Random Harmonic Series

Random Harmonic Series

Here the positive and negative terms partly cancel, allowing the series to converge. To a probabilist, this alternating series suggests choosing plus and minus signs at random, by tossing a fair coin. Formally, let (εj) ∞ j=1 be independent random variables with common distribution P (εj = 1) = P (εj = −1) = 1/2. Then, Kolmogorov’s three series theorem [1, Theorem 22.8] or the martingale conver...

\random" Random Matrix Products