Conformally Invariant Processes in the Plane

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American Mathematical Society, 2005 - Mathematics - 242 pages
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Theoretical physicists have predicted that the scaling limits of many two-dimensional lattice models in statistical physics are in some sense conformally invariant. This belief has allowed physicists to predict many quantities for these critical systems. The nature of these scaling limits has recently been described precisely by using one well-known tool, Brownian motion, and a new construction, the Schramm-Loewner evolution (SLE). This book is an introduction to the conformally invariant processes that appear as scaling limits. The following topics are covered: stochastic integration; complex Brownian motion and measures derived from Brownian motion; conformal mappings and univalent functions; the Loewner differential equation and Loewner chains; the Schramm-Loewner evolution (SLE), which is a Loewner chain with a Brownian motion input; and applications to intersection exponents for Brownian motion.

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About the author (2005)

Gregory F. Lawler is Professor of Mathematics and Statistics at the University of Chicago. He received the George Polya Prize in 2006 for his work with Oded Schramm and Wendelin Werner.

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