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Author :
Release : 2012-04-06
Genre :
Kind : eBook
Book Rating : 355/5 ( reviews)
Book Synopsis Conformal Invariance by :
Download or read book Conformal Invariance written by . This book was released on 2012-04-06. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Malte Henkel
Release : 2012-04-04
Genre : Language Arts & Disciplines
Kind : eBook
Book Rating : 333/5 ( reviews)
Book Synopsis Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution by : Malte Henkel
Download or read book Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution written by Malte Henkel. This book was released on 2012-04-04. Available in PDF, EPUB and Kindle. Book excerpt: Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE’s conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE’s use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.
Author : Malte Henkel
Release : 2012-04-05
Genre : Science
Kind : eBook
Book Rating : 341/5 ( reviews)
Book Synopsis Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution by : Malte Henkel
Download or read book Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution written by Malte Henkel. This book was released on 2012-04-05. Available in PDF, EPUB and Kindle. Book excerpt: Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE’s conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE’s use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.
Author : Pierluigi Contucci
Release : 2017
Genre : Science
Kind : eBook
Book Rating : 107/5 ( reviews)
Book Synopsis Advances in Disordered Systems, Random Processes and Some Applications by : Pierluigi Contucci
Download or read book Advances in Disordered Systems, Random Processes and Some Applications written by Pierluigi Contucci. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unified perspective on the study of complex systems with contributions written by leading scientists from various disciplines, including mathematics, physics, computer science, biology, economics and social science. It is written for researchers from a broad range of scientific fields with an interest in recent developments in complex systems.
Author : Samuel Stewart Watson
Release : 2015
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Conformal Loop Ensembles and the Gaussian Free Field by : Samuel Stewart Watson
Download or read book Conformal Loop Ensembles and the Gaussian Free Field written by Samuel Stewart Watson. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: The study of two-dimensional statistical physics models leads naturally to the analysis of various conformally invariant mathematical objects, such as the Gaussian free field, the Schramm-Loewner evolution, and the conformal loop ensemble. Just as Brownian motion is a scaling limit of discrete random walks, these objects serve as universal scaling limits of functions or paths associated with the underlying discrete models. We establish a new convergence result for percolation, a well-studied discrete model. We also study random sets of points surrounded by exceptional numbers of conformal loop ensemble loops and establish the existence of a random generalized function describing the nesting of the conformal loop ensemble. Using this framework, we study the relationship between Gaussian free field extrema and nesting extrema of the ensemble of Gaussian free field level loops. Finally, we describe a coupling between the set of all Gaussian free field level loops and a conformal loop ensemble growth process introduced by Werner and Wu. We prove that the dynamics are determined by the conformal loop ensemble in this coupling, and we use this result to construct a conformally invariant metric space.
