Jerry Buckley (King's College)

Fluctuations in the increment of the argument for the GEF

The Gaussian entire function (GEF) is a random entire function, characterised by a certain invariance with respect to isometries of the plane. I will explain this invariance, and then study the fluctuations of the increment of the argument of the GEF along planar curves. We will describe the limiting covariance, in terms of an 'inner product' on the 'space' of curves, which we call the signed length. We also establish asymptotic normality. Joint work with Mikhail Sodin.