Aspects of Spatially-Correlated Random Fields: Extreme-Value Statistics and Clustering Properties

Abstract

Rare events of large-scale spatially-correlated exponential random fields are studied. The influence of spatial correlations on clustering and non-sphericity is investigated. The size of the performed simulations permits to study beyond-$7.5$-sigma events (one in $10^{13}$). As an application, this allows to resolve individual Hubble patches which fulfil the condition for primordial black hole formation. It is argued that their mass spectrum is drastically altered due to co-collapse of clustered overdensities as well as the mutual threshold-lowering through the latter. Furthermore, the corresponding non-sphericities may imply possibly large changes in the initial black hole spin distribution.

8 pages, 7 figures; v2: changes to match published version

References in corpus (19)

• Planck 2018 results. X. Constraints on inflation
• Did LIGO detect dark matter?
• Binary Black Hole Mergers in the first Advanced LIGO Observing Run
• Primordial Black Holes as Dark Matter: Recent Developments
• Multiscale Gaussian Random Fields for Cosmological Simulations
• Universality Classes for Extreme Value Statistics
• Black hole formation in the Friedmann universe: Formulation and computation in numerical relativity
• Primordial black hole formation in the early universe: critical behaviour and self-similarity
• Primordial black hole formation in the radiative era: investigation of the critical nature of the collapse
• Cosmic Conundra Explained by Thermal History and Primordial Black Holes
• The exponential tail of inflationary fluctuations: consequences for primordial black holes
• Primordial Black Holes from Inflation and Quantum Diffusion
• The Clustering Evolution of Primordial Black Holes
• Weighted principal component analysis: a weighted covariance eigendecomposition approach
• Statistics of coarse-grained cosmological fields in stochastic inflation
• General Statistical properties of the CMB Polarization field
• Primordial Black Hole formation from overlapping cosmological fluctuations
• The statistics of peaks of weakly non-Gaussian random fields: Effects of bispectrum in two- and three-dimensions
• Statistics of non-polarized points in the CMB polarization maps