Random waves are used as models of chaotic billiard systems. On large scales they equidistribute. However if we look at numerical simulations (such as the one to the left provided by Alex Barnett) we see that there appear to be small scale enhancements along some lines.

In this project we are focused on understanding this (and other) small scale structure of random waves. When does it exist? Exactly how large are the enhancements? Is there any structure to them?