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 Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2015
|
| Series: | Institute of Mathematical Statistics textbooks
5 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xvii, 203 pages) |
| ISBN: | 9781139924160 |
| DOI: | 10.1017/CBO9781139924160 |
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| id | DE-604.BV043940245 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:13Z |
| institution | BVB |
| isbn | 9781139924160 |
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| spelling | Garban, Christophe 1982- Verfasser aut Noise sensitivity of boolean functions and percolation Christophe Garban, ICJ, Université Lyon, Jeffrey E. Steif, Chalmers University of Technology, Gothenberg Noise Sensitivity of Boolean Functions & Percolation Cambridge Cambridge University Press 2015 1 online resource (xvii, 203 pages) txt rdacontent c rdamedia cr rdacarrier Institute of Mathematical Statistics textbooks 5 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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. Sonstige oth Erscheint auch als Druckausgabe 978-1-107-07643-3 Erscheint auch als Druckausgabe 978-1-107-43255-0 https://doi.org/10.1017/CBO9781139924160 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Garban, Christophe 1982- Noise sensitivity of boolean functions and percolation Statistical physics / Textbooks Percolation (Statistical physics) / Textbooks Algebra, Boolean / Textbooks |
| title | Noise sensitivity of boolean functions and percolation |
| title_alt | Noise Sensitivity of Boolean Functions & 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 |
| url | https://doi.org/10.1017/CBO9781139924160 |
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