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math.PR2019★ 15 cited
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…
math.PR2019★ 9 cited
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…