Robert Adler
Faculty of Industrial Engineering and Management
Technion, ISRAEL, 32000
ie.technion.ac.il/Adler.phtml
Why do plankton cells aggregate: a view from superprocesses
Once upon a time, there was a random walk. As time went on, it became normalised in space and time, and, eventually, it converged to Brownian motion. Almost immediately, it was recognised by both theoreticians and researchers in a wide variety of disciplines that Brownian motion was a "good thing" to understand and to use as a real model.
More recently, there was a branching random walk, which, using their experience, probabilists immediately speeded up and normalised. The result, they (eventually) agreed to call "super Brownian motion". Almost immediately, they realised that super Brownian motion was also a "good thing" and spent much of the 1990's studying it.
Somewhat surprising the probabilists, it is turning out that super Brownian motion, in particular, and superprocesses, in general, may actually provide a valuable modelling tool for understanding the motion of high density, temporally and spatially evolving populations. In particular, they provide a natural framework for the "clumping" phenomena often seen in such populations.
This expository talk is designed to show why such is the case. It will include some formulae, lots of pictures, and a movie or two.