43 citations · 130 across the 29 of their papers we have counts for
5 papers · 2 filters
Percolation of the excursion sets of planar symmetric shot noise fields
Raphaël Lachièze-Rey, Stephen Muirhead
We prove the existence of phase transitions in the global connectivity of the excursion sets of planar symmetric shot noise fields. Our main result establishes a phase transition w…
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…
Mean conservation of nodal volume and connectivity measures for Gaussian ensembles
Dmitry Beliaev, Stephen Muirhead, Igor Wigman
We study in depth the nesting graph and volume distribution of the nodal domains of a Gaussian field, which have been shown in previous works to exhibit asymptotic laws. A striking…
A second moment bound for critical points of planar Gaussian fields in shrinking height windows
Stephen Muirhead
We consider the number of critical points of a stationary planar Gaussian field, restricted to a large domain, whose heights lie in a certain interval. Asymptotics for the mean of…