43 citations · 130 across the 29 of their papers we have counts for
37 papers
Poisson approximation of the largest gaps between zeros of a stationary Gaussian process
Renjie Feng, Stephen Muirhead
We study the largest gaps between successive zeros of a smooth stationary Gaussian process. Our main result is that, if correlations decay at least polynomially, then after suitabl…
Sign-balance of random Laplace eigenfunctions
Stephen Muirhead, Igor Wigman
Motivated by the problem of the small-scale sign distribution of Laplace eigenfunctions, we introduce a strong notion of sign-balance for (eigen)functions, and prove that random ei…
The maximum of a strongly correlated Gaussian process
Jason Li, Stephen Muirhead
We revisit a result of Mittal--Ylvisaker that states that the rescaled maximum of a stationary sequence of Gaussian random variables has a Gaussian limit if correlations decay suff…
Persistence and entropic repulsion of stationary Gaussian fields with spectral singularity at the origin
Naomi Feldheim, Ohad Feldheim, Stephen Muirhead
We compute the exact log-asymptotics of the persistence probability, and determine the entropic repulsion profile conditioned on persistence, for general -dimensional stationary…
Limit theorems for the number of sign and level-set clusters of the Gaussian free field
Michael McAuley, Stephen Muirhead
We study the limiting fluctuations of the number of sign and level-set clusters of the Gaussian free field on , , that are contained in a large domain. In di…
The giant component of excursion sets of spherical Gaussian ensembles: existence, uniqueness, and volume concentration
Stephen Muirhead, Igor Wigman
We establish the existence and uniqueness of a well-concentrated giant component in the supercritical excursion sets of three important ensembles of spherical Gaussian random field…
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 sprinkled decoupling inequality for Gaussian processes and applications
Stephen Muirhead
We establish a sprinkled decoupling inequality for increasing events of Gaussian vectors with an error that depends only on the maximum pairwise correlation. As an application we p…
Percolation of strongly correlated Gaussian fields II. Sharpness of the phase transition
Stephen Muirhead
We establish the sharpness of the phase transition for a wide class of Gaussian percolation models, on or , , with correlations decaying at le…
Percolation of strongly correlated Gaussian fields I. Decay of subcritical connection probabilities
Stephen Muirhead, Franco Severo
We study the decay of connectivity of the subcritical excursion sets of a class of strongly correlated Gaussian fields. Our main result shows that, for smooth isotropic Gaussian fi…
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…
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…
Asymptotics for the critical level and a strong invariance principle for high intensity shot noise fields
Raphael Lachieze-Rey, Stephen Muirhead
We study fine properties of the convergence of a high intensity shot noise field towards the Gaussian field with the same covariance structure. In particular we (i) establish a str…
Boundedness of the nodal domains of additive Gaussian fields
Stephen Muirhead
We study the connectivity of the excursion sets of additive Gaussian fields, i.e.\ stationary centred Gaussian fields whose covariance function decomposes into a sum of terms that…
Mean-field bounds for Poisson-Boolean percolation
Vivek Dewan, Stephen Muirhead
We establish the mean-field bounds , and on the critical exponents of the Poisson-Boolean continuum percolation model under a moment condition on…
Upper bounds on the one-arm exponent for dependent percolation models
Vivek Dewan, Stephen Muirhead
We prove upper bounds on the one-arm exponent for a class of dependent percolation models which generalise Bernoulli percolation; while our main interest is level set percola…
The phase transition for planar Gaussian percolation models without FKG
Stephen Muirhead, Alejandro Rivera, Hugo Vanneuville +1
We develop techniques to study the phase transition for planar Gaussian percolation models that are not (necessarily) positively correlated. These models lack the property of posit…
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…
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…