15 citations · 40 across the 6 of their papers we have counts for
6 papers
Conformal welding of independent Gaussian multiplicative chaos measures
Antti Kupiainen, Michael McAuley, Eero Saksman
We solve the classical conformal welding problem for a composition of two random homeomorphisms generated by independent Gaussian multiplicative chaos measures with small parameter…
A covariance formula for the number of excursion set components of Gaussian fields and applications
Dmitry Beliaev, Michael McAuley, Stephen Muirhead
We derive a covariance formula for the number of excursion or level set components of a smooth stationary Gaussian field on contained in compact domains. We also pre…
A central limit theorem for the number of excursion set components of Gaussian fields
Dmitry Beliaev, Michael McAuley, Stephen Muirhead
For a smooth stationary Gaussian field on and level , we consider the number of connected components of the excursion set (or l…
Fluctuations of the number of excursion sets of planar Gaussian fields
Dmitry Beliaev, Michael McAuley, Stephen Muirhead
For a smooth, stationary, planar Gaussian field, we consider the number of connected components of its excursion set (or level set) contained in a large square of area . The m…
Smoothness and monotonicity of the excursion set density of planar Gaussian fields
Dmitry Beliaev, Michael McAuley, Stephen Muirhead
Nazarov and Sodin have shown that the number of connected components of the nodal set of a planar Gaussian field in a ball of radius , normalised by area, converges to a constan…
On the number of excursion sets of planar Gaussian fields
Dmitry Beliaev, Michael McAuley, Stephen Muirhead
The Nazarov-Sodin constant describes the average number of nodal set components of Gaussian fields on large scales. We generalise this to a functional describing the corresponding…