# Continuum preferential attachment, volume 2

Awhile ago—in fact, too long ago—I noted that Peter Dodds and I were working on a short paper regarding continuum preferential attachment processes. Well, here it is. We submitted it to Physical Review E and got a “reject with resubmit” late last fall; I haven’t yet had a chance to resubmit.

To recap: we construct a continuum (read: PDE) mean-field model for preferential attachment processes and solve it in all generality. Because we didn’t have anything better to do, we then extended this process to $$N \geq 1$$ dimensions. We then note that the power-law distribution of firm sizes in the US can be partially explained by such a process. While it is well-known that a power law fits this data, a theoretical explanation was not known to us; we propose a simple economic model here that reproduces this phenomenon.

Let me know if you have any suggestions for the resubmit!

Written on February 19, 2018