Trevor Johnson

Large-Parameter Asymptotics of Laguerre Rational Solutions to Painleve V

The Painleve equations arise naturally in real-world systems, often describing what happens at the boundary between different types of behavior. They appear, for example, at the transition between water waves and ripples, at the critical temperature where materials lose their magnetization, and at the sharp edge between typical and extremely rare statistical outcomes. However, Painleve equation solutions are too complicated in practice. This project develops approximations of the Laguerre rational solutions to Painleve V, which have applications to the Laguerre Unitary Ensemble of random matrices, and is used in detecting signals from noisy data and predicting the performance of multi-antenna wireless communication systems.