Stephen Muirhead

Upper bounds on the one-arm exponent for dependent percolation models

V Dewan, S Muirhead

Journal article  |  2023  |  Probability Theory and Related Fields

We prove upper bounds on the one-arm exponent η1 for a class of dependent percolation models which generalise Bernoulli percolatio..

Mean-field bounds for Poisson-Boolean percolation

V Dewan, S Muirhead

Journal article  |  2023  |  Electronic Journal of Probability

We establish the mean-field bounds γ ≥ 1, δ ≥ 2 and △ ≥ 2 on the critical exponents of the Poisson-Boolean continuum percolation m..

Fluctuations of the number of excursion sets of planar Gaussian fields

Dmitry Beliaev, Michael McAuley, Stephen Muirhead

Journal article  |  2022  |  Probability and Mathematical Physics

Percolation of the excursion sets of planar symmetric shot noise fields

Raphael Lachieze-Rey, Stephen Muirhead

Journal article  |  2022  |  Stochastic Processes and their Applications

We prove the existence of phase transitions in the global connectivity of the excursion sets of planar symmetric shot noise fields..

Sharp phase transition for Cox percolation

C Hirsch, B Jahnel, S Muirhead

Journal article  |  2022  |  Electronic Communications in Probability

We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percol..

BOUNDEDNESS OF THE NODAL DOMAINS OF ADDITIVE GAUSSIAN FIELDS

S Muirhead

Journal article  |  2022  |  Theory of Probability and Mathematical Statistics

We study the connectivity of the excursion sets of additive Gaussian fields, i.e. stationary centred Gaussian fields whose covaria..

Russo–Seymour–Welsh estimates for the Kostlan ensemble of random polynomials

D Beliaev, S Muirhead, I Wigman

Journal article  |  2021  |  Annales de l'institut Henri Poincare (B) Probability and Statistics

Beginning with the predictions of Bogomolny–Schmit for the random plane wave, in recent years the deep connections between the lev..

Mean conservation of nodal volume and connectivity measures for Gaussian ensembles

Dmitry Beliaev, Stephen Muirhead, Igor Wigman

Journal article  |  2021  |  Advances in Mathematics

We study in depth the nesting graph and volume distribution of the nodal domains of a Gaussian field, which have been shown in pre..

The band structure of a model of spatial random permutation

Yan V Fyodorov, Stephen Muirhead

Journal article  |  2021  |  PROBABILITY THEORY AND RELATED FIELDS

We study a random permutation of a lattice box in which each permutation is given a Boltzmann weight with energy equal to the tota..

On the number of excursion sets of planar Gaussian fields

D Beliaev, M McAuley, S Muirhead

Journal article  |  2020  |  Probability Theory and Related Fields

The Nazarov–Sodin constant describes the average number of nodal set components of smooth Gaussian fields on large scales. We gene..