Talk by Martin Barlow, Mathematics and 2009 Distinguished Scholar in Residence
'Randomness' and 'structure' may seem contradictory concepts; but many large scale random systems also have interesting structures. In this talk I will discuss two models of random phenomena, and the types of structure they exhibit.
The first, random walks, describes the motion of a particle which moves in space 'at random'. Significant work was done in the early 20th century: in particular random walks and their continuum limits were used by Einstein to study Brownian motion, and Bachelier to study stock prices. The second model is 'percolation', which was introduced by Broadbent and Hammersley in 1957. This describes a network with random connections: one motivation was to describe obstructions to the flow of gas through the carbon filter in a gas mask. Percolation arises in many other contexts: one example is that of the 'contact networks' used to describe the spread of disease in a community.
Though both models can be described easily, many questions remain unsolved: I will mention some of these. Finally, I will discuss what happens when one combines the two models.
Dinner and talk 6:30 to 9:00 pm, but welcome at 6:00 pm reception.