As a student, he took part in the first three International Mathematical Olympiads , winning two gold medals. However, the authorities denied his request to return to Cambridge for doctoral study. A similar scholarship offer from Paris was also quashed. After spending a year at Christ Church, Oxford , where Michael Atiyah held the Savilian Chair of Geometry, he vowed never to return to Hungary due to his disillusion with the Soviet intervention. He then went to Trinity College, Cambridge , where in he received a second PhD in functional analysis , studying Banach algebras under the supervision of Frank Adams.
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It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book, first published in , are twofold. First to present classical results in a way that is accessible to non-specialists. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory.
Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.
Table of contents Preface; 1. Basic concepts; 2. Probabilistic tools; 3. Percolation on Z2 - the Harris-Kesten theorem; 4. Uniqueness of the infinite open cluster and critical probabilities; 6. Estimating critical probabilities; 7. Conformal invariance - Smirnov's theorem; 8. Continuum percolation; Bibliography; Index; List of notation. Review quote 'This book contains a complete account of most of the important results in the fascinating area of percolation.
Elegant and straightforward proofs are given with minimal background in probability or graph theory. It is self-contained, accessible to a wide readership and widely illustrated with numerous examples. It will be of considerable interest for both beginners and advanced searchers alike. A useful addition for its focus on the recent advances in two-dimensional percolation He has held visiting positions from Seattle to Singapore, from Brazil to Zurich.
This is his eleventh book. Rating details. Book ratings by Goodreads. Goodreads is the world's largest site for readers with over 50 million reviews.
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