Since perturbations δ δ M are Gaussian distributed with an average 0 and variance σ σ ( M ) , we can directly compute the probability of halos forming with masses at least M as f ( δ δ M > δ δ c ) = ∫ ∫ δ δ c ∞ ∞ d δ δ M 1 2 π π σ σ ( M ) exp ⁡ ⁡ ( − − 1 2 δ δ M 2 σ σ 2 ( M ) ) = 1 2 erfc ⁡ ⁡ ( 1 2 δ δ c σ σ ( M ) ) .