Noise Sensitivity of Boolean Functions and Percolation

Informationen zum Autor Christophe Garban is a professor of mathematics at Université Lyon I, France. Klappentext This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation. Zusammenfassung 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. Inhaltsverzeichnis 1. Boolean functions and key concepts; 2. Percolation in a nutshell; 3. Sharp thresholds and the critical point; 4. Fourier analysis of Boolean functions; 5. Hypercontractivity and its applications; 6. First evidence of noise sensitivity of percolation; 7. Anomalous fluctuations; 8. Randomized algorithms and noise sensitivity; 9. The spectral sample; 10. Sharp noise sensitivity of percolation; 11. Applications to dynamical percolation; 12. For the connoisseur; 13. Further directions and open problems.

Product details

• Authors: Christophe Garban, Christophe (Universite Lyon I) Garban, Christophe (Universite Lyon I) Steif Garban, Christophe Steif Garban, Jeffrey E Steif, Jeffrey E. Steif, Jeffrey E. (Chalmers University of Technology Steif
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 22.12.2014
• EAN: 9781107076433
• ISBN: 978-1-107-07643-3
• No. of pages: 222
• Series: Institute of Mathematical Statistics Textbooks; Institute of Mathematical Statistics Textbooks; Institute of Mathematical Stat
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis