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Excursion sets: follow the first threshold crossing to avoid nested double counting

Contribution grade

Astronomy · Astronomy

Reference score190,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Bond, Cole, Efstathiou and Kaiser replace single-scale threshold counting with first crossings across smoothing scales, derive the Press-Schechter factor of two for sharp-k Gaussian walks, and extend the framework to conditional mass histories.

Scientific scope

Bond, Cole, Efstathiou and Kaiser replace single-scale threshold counting with first crossings across smoothing scales, derive the Press-Schechter factor of two for sharp-k Gaussian walks, and extend the framework to conditional mass histories. The halo mapping assumes a homogeneous isotropic Gaussian initial field and a specified collapse threshold. Sharp-k filtering supplies independent increments and the Brownian first-crossing calculation; other filters produce correlated, non-Markov histories and require approximations or numerics. Filter-radius/mass calibration and finite simulation comparisons have limits. This is not an exact physical collapse theory, complete merger-history model or independently verified prediction for every mass range.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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