Conformally Invariant Processes in the Plane (Mathematical

Conformally Invariant Processes in the Plane (Mathematical Surveys and Monographs)

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. The prerequisites are first-year graduate courses in real analysis, complex analysis, and probability. The book is suitable for graduate students and research mathematicians interested in random processes and their applications in theoretical physics.

Country	USA
Author	Gregory F. Lawler
Binding	Paperback
EAN	9780821846247
ISBN	0821846248
Label	American Mathematical Society
Manufacturer	American Mathematical Society
NumberOfItems	1
NumberOfPages	242
PublicationDate	2008-05-21
Publisher	American Mathematical Society
SKU	M0821846248
Studio	American Mathematical Society
ReleaseDate	0000-00-00

Conformally Invariant Processes in the Plane (Mathematical Surveys and Monographs)