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Abstract |
Generally, Brownian motion is the scaling limit of simple random walk and especially in dimension two it has an very important property-conformal invariance. Except for the Brownian motion, theoretical physicists have predicted that the scaling limits of many two-dimensional lattice models are also in some sense conformally invariant. The nature of these scaling limits has been recently described using the well-known tool, Brownian motion and a new construction, the Schramm-Loewner evolution. One of the application of this theory is computation of the exact value of the Hausdorff dimension of some exceptional sets about planar Brownian motion. So here we will give an introduction tolzli the following topics:
1 Brownian motion and its main properties
2 Some discrete models and their scaling limits
3 Conformal invariant property of the scaling limits and their applications |
