## View abstract

### Session S33 - Spectral Geometry

Wednesday, July 21, 17:30 ~ 17:50 UTC-3

## Filament structure in random plane waves

### Melissa Tacy

Numerical studies of random plane waves, functions $u=\sum_{j}c_{j}e^{\frac{i}{h}\langle x,\xi_{j}\rangle}$ where the coefficients $c_{j}$ are chosen at random'', have detected an apparent filament structure. The waves appear enhanced along straight lines. There has been significant difference of opinion as to whether this structure is indeed a failure to equidistribute, numerical artefact or an illusion created by the human desire to see patterns. In this talk I will present some recent results that go some way to answering the question. We study the behaviour of a random variable $G(x,\xi)=||P_{(x,\xi)}u||_{L^{2}}$ where $P_{(x,\xi)}$ is a semiclassical localiser at Planck scale around $(x,\xi)$ and show that $G(x,\xi)$ fails to equidistribute. This suggests that the observed filament structure is a configuration space reflection of the phase space concentrations.