= Razor-thin disk relaxation
{title2=$t_{\rm rel}\sim\lambda t_{\rm dyn}$}
In an unsoftened <plane> with number surface density $n_2$ and relative <speed> $u$, an encounter strip has area $2u\,dt\,db$. Thus the <velocity> diffusion rate is $8G^2m^2n_2/u\int db/b^2$, dominated by the small-impact cutoff. Setting this cutoff to $Gm/u^2$ and requiring a change of order $u^2$ gives $t_{\rm rel}\sim u/(Gmn_2)$. With $u=\lambda v$, $n_2\sim N/R^2$ and $v^2\sim GNm/R$, this is of order $\lambda R/v$, independent of $N$ at fixed total <mass>. The point-particle, zero-thickness limit is singular; fixed softening or nonzero thickness changes it. Numerical coefficients are not controlled by extending weak kicks down to order-one deflections.
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