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# Richard Kenyon : Random maps from **Z**^{2} to **Z**

^{2}

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 **Z ^{2}**
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

**Z**to

^{2}**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

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