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!