Excursion-set description of halo formation
= Excursion-set description of halo formation
A halo is associated with the first upcrossing of the <linear spherical-collapse threshold> by the smoothed <density contrast> as its variance increases. With a <sharp-k smoothing filter>, the <Brownian reflection principle> makes the crossing probability twice the one-scale Gaussian upper tail. This handles trajectories that crossed earlier but finish below the barrier and leads to the <Press-Schechter halo mass function>.