10 citations · 17 across the 12 of their papers we have counts for
5 papers · 1 filter
Coupling of stationary fields with application to arithmetic waves
Dmitry Beliaev, Riccardo W. Maffucci
In this paper we obtain a range of quantitative results of the following type: given two centered Gaussian fields with close covariance kernels we construct a coupling such that th…
No repulsion between critical points for planar Gaussian random fields
Dmitry Beliaev, Valentina Cammarota, Igor Wigman
We study the behaviour of the point process of critical points of isotropic stationary Gaussian fields. We compute the main term in the asymptotic expansion of the two-point correl…
Intermediate and small scale limiting theorems for random fields
Dmitry Beliaev, Riccardo W. Maffucci
In this paper we study the nodal lines of random eigenfunctions of the Laplacian on the torus, the so called 'arithmetic waves'. To be more precise, we study the number of intersec…
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…