= Power-law Press-Schechter stellar mass function
{title2=$n_*(M_*)\propto M_*^{\beta-2}e^{-(M_*/M_{*,\rm ch})^{2\beta}}$}
For a power-law matter spectrum, smoothed variance scales as $\sigma\propto M^{-\beta}$ with $\beta=(n+3)/6$. Differentiating the Press-Schechter collapsed fraction gives a halo mass function proportional to $M^{\beta-2}\exp[-(M/M_{h,\rm ch})^{2\beta}]$. A constant <stellar-to-halo mass ratio> preserves both exponents and rescales characteristic mass and normalization.
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