2 citations · 2 across the 3 of their papers we have counts for
8 papers
Sharp phase transition for Cox percolation
Christian Hirsch, Benedikt Jahnel, Stephen Muirhead
We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirement…
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…
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…
The band structure of a model of spatial random permutation
Yan V. Fyodorov, Stephen Muirhead
We study a random permutation of a lattice box in which each permutation is given a Boltzmann weight with energy equal to the total Euclidean displacement. Our main result establis…