Richard Kenyon : Random maps from Z² to Z (Jan 16, 2001 4:00 PM)

One of the most basic objects in probability theory is the simple random walk, which one can think of as a random map from Z to Z mapping adjacent points to adjacent points. A similar theory for random maps from Z² to Z had until recently remained elusive to mathematicians, despite being known (non-rigorously) to physicists. In this talk we discuss some natural families of random maps from Z² to Z. We can explicitly compute both the local and the large-scale behavior of these maps. In particular we construct a "scaling limit" for these maps, in a similar sense in which Brownian motion is a scaling limit for the simple random walk. The results are in accord with physics.

• Category: Other Meetings and Events
• Duration: 01:08:52
• Date:  January 16, 2001 at 4:00 PM
• Views: 40
• Tags:   seminar, Special Lecture