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Noise Sensitivity of Boolean Functions and Percolation (Institute of Mathematical Statistics Textbooks, Series Number 5) - Softcover
Synopsis
This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the now-famous Schramm-Loewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourier-analytic setup, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging.
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Book Description
This account of the new and exciting area of noise sensitivity of Boolean functions - in particular applied to critical percolation - is designed for graduate students and researchers in probability theory, discrete mathematics, and theoretical computer science. It assumes a basic background in probability theory and integration theory. Each chapter ends with exercises.
About the Author
Christophe Garban is a professor of mathematics at Université Lyon I, France.
"About this title" may belong to another edition of this title.
- PublisherCambridge University Press
- Publication date2014
- ISBN 10 1107432553
- ISBN 13 9781107432550
- BindingPaperback
- LanguageEnglish
- Number of pages222
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Noise Sensitivity of Boolean Functions and Percolation (Institute of Mathematical Statistics Textbooks)
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Noise Sensitivity of Boolean Functions and Percolation
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Noise Sensitivity of Boolean Functions and Percolation (Institute of Mathematical Statistics Textbooks, Series Number 5)
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ISBN 13: 9781107432550
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Noise Sensitivity of Boolean Functions and Percolation (Institute of Mathematical Statistics Textbooks, Series Number 5)
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ISBN 10: 1107432553
ISBN 13: 9781107432550
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Noise Sensitivity of Boolean Functions and Percolation (Paperback)
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ISBN 10: 1107432553
ISBN 13: 9781107432550
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Paperback. Condition: new. Paperback. This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the now-famous Schramm-Loewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourier-analytic set-up, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging. This account of the new and exciting area of noise sensitivity of Boolean functions - in particular applied to critical percolation - is designed for graduate students and researchers in probability theory, discrete mathematics, and theoretical computer science. It assumes a basic background in probability theory and integration theory. Each chapter ends with exercises. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781107432550
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Noise Sensitivity of Boolean Functions and Percolation (Institute of Mathematical Statistics Textbooks, Series Number 5)
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ISBN 10: 1107432553
ISBN 13: 9781107432550
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Noise Sensitivity of Boolean Functions and Percolation
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the now-famous Schramm-Loewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourier-analytic set-up, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging. Seller Inventory # 9781107432550
Quantity: 1 available