Noise sensitivity of Boolean functions and percolation
- Christophe Garban (ICJ, Université Lyon 1, Lyon), Jeffrey E. Steif (Chalmers University of Technology, Gothenburg).
- New York, NY : Cambridge University Press, 2015.
- Copyright notice
- Physical description
- xvii, 203 pages : illustrations ; 24 cm.
- Institute of Mathematical Statistics textbooks ; 5.
At the library
Science Library (Li and Ma)
|QC174.8 .G36 2015||Unknown|
- Includes bibliographical references (pages 197-202) and index.
- 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.
- (source: Nielsen Book Data)
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.
(source: Nielsen Book Data)
- Publication date
- Copyright date
- Institute of Mathematical Statistics textbooks ; 5
- 9781107076433 hardback
- 1107076439 hardback
- 9781107432550 pbk.
- 1107432553 pbk.
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