Probability Seminars

## Dimensions of the two-valued sets of the 2D GFF

### With Lukas Schoug (Cambridge)

# Dimensions of the two-valued sets of the 2D GFF

The two-valued sets of the two-dimensional Gaussian free field

(GFF) are local sets such that the associated harmonic function takes

only two values. In this talk, we describe how to compute the almost

sure Hausdorff dimension of these sets. A central tool is the imaginary

multiplicative chaos, that is, the random element exp(ic h(z)), where h

is a GFF . The talk is based on joint work with Avelio Sepulveda and

Fredrik Viklund.

- Speaker: Lukas Schoug (Cambridge)
- Tuesday 27 October 2020, 14:00–15:00
- Venue: https://maths-cam-ac-uk.zoom.us/j/5903322638?pwd=dzJRRS9BKzhEaGVCNncxaWcvL0IxQT09.
- Series: Probability; organiser: Perla Sousi.