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

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 ($1$ in $10^{13}$). As an application, this allows to resolve individual Hubble patches which fulfill 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 imply possibly large changes in the initial black hole spin distribution.