Gregory F Lawler 
Conformally Invariant Processes in the Plane [PDF ebook] 

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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. Such a belief has allowed them to predict many quantities for these critical systems. The nature of these scaling limits has recently been described precisely 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. Topics include: 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 whose input is a Brownian motion; application to intersection exponents for Brownian motion. The prerequisites are first-year graduate courses in real analysis, complex analysis, and probability.

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Format PDF ● Strony 242 ● ISBN 9781470413415 ● Wydawca American Mathematical Society ● Do pobrania 3 czasy ● Waluta EUR ● ID 6613613 ● Ochrona przed kopiowaniem Adobe DRM
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