Noise Sensitivity of Boolean Functions and Percolation

Nonfiction, Science & Nature, Mathematics, Statistics, Science
Cover of the book Noise Sensitivity of Boolean Functions and Percolation by Christophe Garban, Jeffrey E. Steif, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Christophe Garban, Jeffrey E. Steif ISBN: 9781316120620
Publisher: Cambridge University Press Publication: December 22, 2014
Imprint: Cambridge University Press Language: English
Author: Christophe Garban, Jeffrey E. Steif
ISBN: 9781316120620
Publisher: Cambridge University Press
Publication: December 22, 2014
Imprint: Cambridge University Press
Language: English

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.

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

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.

More books from Cambridge University Press

Cover of the book A History of Thailand by Christophe Garban, Jeffrey E. Steif
Cover of the book The Cambridge Companion to Caryl Churchill by Christophe Garban, Jeffrey E. Steif
Cover of the book Cambridge Handbook of Research Approaches to Business Ethics and Corporate Responsibility by Christophe Garban, Jeffrey E. Steif
Cover of the book Sociological Studies in Roman History by Christophe Garban, Jeffrey E. Steif
Cover of the book Human Trafficking by Christophe Garban, Jeffrey E. Steif
Cover of the book Why Switzerland? by Christophe Garban, Jeffrey E. Steif
Cover of the book The Cambridge Companion to Conducting by Christophe Garban, Jeffrey E. Steif
Cover of the book Theoderic and the Roman Imperial Restoration by Christophe Garban, Jeffrey E. Steif
Cover of the book The Foundations of the Modern Philippine State by Christophe Garban, Jeffrey E. Steif
Cover of the book Fundamentals of Linear Control by Christophe Garban, Jeffrey E. Steif
Cover of the book 5G Mobile and Wireless Communications Technology by Christophe Garban, Jeffrey E. Steif
Cover of the book The Peasant in Postsocialist China by Christophe Garban, Jeffrey E. Steif
Cover of the book World Literature and the Geographies of Resistance by Christophe Garban, Jeffrey E. Steif
Cover of the book The Iraq Wars and America's Military Revolution by Christophe Garban, Jeffrey E. Steif
Cover of the book The Genre of Acts and Collected Biography by Christophe Garban, Jeffrey E. Steif
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