Schramm-Loewner evolution. (2017)

• Record Type: Book
• Further Information: Note: Anti Kemppainen.
• Authors: Kemppainen, Antti
• Contents: Introduction -- Iteration of conformal maps -- On stochastic models and connection to statistical physics -- An example: percolation model and Cardy's formula -- On reading this book -- Introduction to stochastic calculus -- Brownian motion -- Stochastic integration -- Itô's formula -- Further topics in stochastic calculus -- Conformal invariance of two-dimensional Brownian motion -- Weak convergence of probability measures -- Introduction to conformal mappings -- Harmonic functions -- Conformal maps -- From Area theorem to distortion -- Conformally invariant tools -- Loewner equation -- Conformal maps of the upper half-plane -- Loewner chains -- Loewner equations in D and Sp -- Schramm-Loewner evolution.-Schramm-Loewner evolution and its elementary properties -- Advanced properties of SLE -- Proofs for some of the advanced properties -- Variants of SLE -- Moments of the derivative of the Loewner map of SLE(k) -- Regularity and convergence of random curves -- Continuity properties of the Loewner chains -- Continuity of SLE(k) -- Convergence of interfaces in the site percolation model -- Index.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource
• Subjects: 530.15/95; Physics; Statistical physics; SCIENCE -- Energy; SCIENCE -- Mechanics -- General; SCIENCE -- Physics -- General; Statistical physics; Science -- Mathematical Physics; Mathematics -- Probability & Statistics -- General; Mathematics -- Mathematical Analysis; Science -- Physics; Mathematical physics; Probability & statistics; Statistical physics; Complex analysis, complex variables; Mathematical physics; Distribution (Probability theory); Differential equations, partial; Electronic books
• Languages: English
• ISBNs: 9783319653297; 3319653296
• Related ISBNs: 9783319653273; 331965327X
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed January 9, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.