43 citations · 130 across the 29 of their papers we have counts for
4 papers · 1 filter
A covariance formula for topological events of smooth Gaussian fields
Dmitry Beliaev, Stephen Muirhead, Alejandro Rivera
We derive a covariance formula for the class of `topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets 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…
The sharp phase transition for level set percolation of smooth planar Gaussian fields
Stephen Muirhead, Hugo Vanneuville
We prove that the connectivity of the level sets of a wide class of smooth centred planar Gaussian fields exhibits a phase transition at the zero level that is analogous to the pha…