DETECTING UNIVERSALITY IN NORTH AMERICAN, JAPANESE, AND WORLDWIDE EARTHQUAKES

Abstract

Random Matrix Theory has been used to answer statistical questions about interacting particle systems found in the real-world for the last century, including models found in statistical mechanics, number theory, biology, and transportation systems. Typical modeling compar isons have considered Poissonian statistics, for non-interacting particle systems, as well as the Wigner surmise, for completely chaotic systems from quantum dynamics. We will adapt this methodology to a statistical modeling project using earthquake data in North America, Japan, and world-wide. We are able to establish earthquake spacings between peak activity in a day in Japan satisfy Wigner surmise statistics, while most of the other models obtained using various methodologies displayed Poissonian statistics. These techniques were employed to ultimately analyze smaller datasets as size can have a large impact on the Kolmogorov-Smirnov test. Further directions, including for the second dataset on solar flares, which was only lightly discussed due to focus being on the earthquakes dataset, were detailed.