An Introduction to Random Interlacements

Business & Finance, Management & Leadership, Operations Research, Nonfiction, Science & Nature, Mathematics, Statistics
Cover of the book An Introduction to Random Interlacements by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov ISBN: 9783319058528
Publisher: Springer International Publishing Publication: May 6, 2014
Imprint: Springer Language: English
Author: Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
ISBN: 9783319058528
Publisher: Springer International Publishing
Publication: May 6, 2014
Imprint: Springer
Language: English

This book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. The model was introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus. Random interlacements is a new percolation model on the d-dimensional lattice. The main results covered by the book include the full proof of the local convergence of random walk trace on the torus to random interlacements and the full proof of the percolation phase transition of the vacant set of random interlacements in all dimensions. The reader will become familiar with the techniques relevant to working with the underlying Poisson Process and the method of multi-scale renormalization, which helps in overcoming the challenges posed by the long-range correlations present in the model. The aim is to engage the reader in the world of random interlacements by means of detailed explanations, exercises and heuristics. Each chapter ends with short survey of related results with up-to date pointers to the literature.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. The model was introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus. Random interlacements is a new percolation model on the d-dimensional lattice. The main results covered by the book include the full proof of the local convergence of random walk trace on the torus to random interlacements and the full proof of the percolation phase transition of the vacant set of random interlacements in all dimensions. The reader will become familiar with the techniques relevant to working with the underlying Poisson Process and the method of multi-scale renormalization, which helps in overcoming the challenges posed by the long-range correlations present in the model. The aim is to engage the reader in the world of random interlacements by means of detailed explanations, exercises and heuristics. Each chapter ends with short survey of related results with up-to date pointers to the literature.

More books from Springer International Publishing

Cover of the book Formal Aspects of Component Software by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book László Zechmeister by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Introduction to Uncertainty Quantification by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Quantum Waveguides by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Neonatal Transfusion Practices by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Computational Complexity of Solving Equation Systems by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Algorithms and Architectures for Parallel Processing by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Next Generation Antibody Drug Conjugates (ADCs) and Immunotoxins by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Toward 5G Software Defined Radio Receiver Front-Ends by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Astronomical Discoveries You Can Make, Too! by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Non-traditional Micromachining Processes by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Crisis Management for Software Development and Knowledge Transfer by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Constraint Solving and Planning with Picat by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Machine Learning Paradigms: Theory and Application by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
Cover of the book Multiscale Modelling in Sheet Metal Forming by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy