Probability Seminars

## Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves

### With Igor Wigman (King’s College, London)

# Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves

This is joint work with Par Kurlberg.

We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for “arithmetic random waves”, i.e. random toral Laplace eigenfunctions.

- Speaker: Igor Wigman (King’s College, London)
- Tuesday 23 January 2018, 16:15–17:15
- Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
- Series: Probability; organiser: Perla Sousi.