Noise sensitivity of Boolean functions and percolation:
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 hyperc...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
[2015]
|
| Series: | Institute of Mathematical Statistics textbooks
5 |
| Subjects: | |
| Summary: | 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 |
| Physical Description: | xvii, 203 Seiten Illustrationen |
| ISBN: | 9781107432550 |
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MARC
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| id | DE-604.BV044798453 |
| illustrated | Illustrated |
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| institution | BVB |
| isbn | 9781107432550 |
| language | English |
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| physical | xvii, 203 Seiten Illustrationen |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Institute of Mathematical Statistics textbooks |
| series2 | Institute of Mathematical Statistics textbooks |
| spelling | Garban, Christophe 1982- (DE-588)1089834888 aut Noise sensitivity of Boolean functions and percolation Christophe Garban, ICJ, Université Lyon ; Jeffrey E. Steif, Chalmers University of Technology, Gothenberg Cambridge Cambridge University Press [2015] © 2015 xvii, 203 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Institute of Mathematical Statistics textbooks 5 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 Statistical physics / Textbooks Percolation (Statistical physics) / Textbooks Algebra, Boolean / Textbooks Steif, Jeffrey E. aut Erscheint auch als Online-Ausgabe 978-1-107-43255-0 Institute of Mathematical Statistics textbooks 5 (DE-604)BV036598560 5 |
| spellingShingle | Garban, Christophe 1982- Steif, Jeffrey E. Noise sensitivity of Boolean functions and percolation Institute of Mathematical Statistics textbooks Statistical physics / Textbooks Percolation (Statistical physics) / Textbooks Algebra, Boolean / Textbooks |
| title | Noise sensitivity of Boolean functions and percolation |
| title_auth | Noise sensitivity of Boolean functions and percolation |
| title_exact_search | Noise sensitivity of Boolean functions and percolation |
| title_full | Noise sensitivity of Boolean functions and percolation Christophe Garban, ICJ, Université Lyon ; Jeffrey E. Steif, Chalmers University of Technology, Gothenberg |
| title_fullStr | Noise sensitivity of Boolean functions and percolation Christophe Garban, ICJ, Université Lyon ; Jeffrey E. Steif, Chalmers University of Technology, Gothenberg |
| title_full_unstemmed | Noise sensitivity of Boolean functions and percolation Christophe Garban, ICJ, Université Lyon ; Jeffrey E. Steif, Chalmers University of Technology, Gothenberg |
| title_short | Noise sensitivity of Boolean functions and percolation |
| title_sort | noise sensitivity of boolean functions and percolation |
| topic | Statistical physics / Textbooks Percolation (Statistical physics) / Textbooks Algebra, Boolean / Textbooks |
| topic_facet | Statistical physics / Textbooks Percolation (Statistical physics) / Textbooks Algebra, Boolean / Textbooks |
| volume_link | (DE-604)BV036598560 |
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