Discretisation schemes for level sets of planar Gaussian fields

DOI10.1007/s00220-018-3084-1zbMath1429.60036arXiv1702.02134OpenAlexW2593611574MaRDI QIDQ1751294

Stephen Muirhead, Dmitri B. Beliaev

Publication date: 25 May 2018

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.02134

zbMATH Keywords

planar Gaussian fieldsRusso-Seymour-Welsh estimates

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15)

Related Items (15)

The critical threshold for Bargmann-Fock percolation ⋮ The sharp phase transition for level set percolation of smooth planar Gaussian fields ⋮ Crossing probabilities for planar percolation ⋮ Equality of critical parameters for percolation of Gaussian free field level sets ⋮ On the excursion area of perturbed Gaussian fields ⋮ The phase transition for planar Gaussian percolation models without FKG ⋮ Sharp phase transition for Gaussian percolation in all dimensions ⋮ Smooth Gaussian fields and percolation ⋮ Bargmann-Fock percolation is noise sensitive ⋮ A covariance formula for topological events of smooth Gaussian fields ⋮ Percolation of random nodal lines ⋮ Talagrand's inequality in planar Gaussian field percolation ⋮ Russo-Seymour-Welsh estimates for the Kostlan ensemble of random polynomials ⋮ Quasi-independence for nodal lines ⋮ Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension \(d\geq 3\)

Cites Work

• Crossing probabilities for Voronoi percolation
• Boundedness of level lines for two-dimensional random fields
• Percolation of random nodal lines
• Conditionally positive definite functions and their application to multivariate interpolations
• Expected number and height distribution of critical points of smooth isotropic Gaussian random fields
• Probabilistic validation of homology computations for nodal domains
• Complexity of Random Energy Landscapes, Glass Transition, and Absolute Value of the Spectral Determinant of Random Matrices
• On the Bogomolny–Schmit conjecture
• Asymptotic Laws for the Spatial Distribution and the Number of Connected Components of Zero Sets of Gaussian Random Functions
• The Geometry of Random Fields
• Level Sets and Extrema of Random Processes and Fields
• On the number of nodal domains of random spherical harmonics
• Regular and irregular semiclassical wavefunctions
• Scattered Data Approximation

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