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Noise Sensitivity of Boolean Functions and Percolation
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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 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.
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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.
Produktdetaljer
Sprog: Engelsk
Sider: 222
ISBN-13: 9781107432550
Indbinding: Paperback
Udgave:
ISBN-10: 1107432553
Kategori: Diskret matematik
Udg. Dato: 22 dec 2014
Længde: 13mm
Bredde: 226mm
Højde: 154mm
Oplagsdato: 22 dec 2014
Forfatter(e) Christophe (Universite Lyon I) Garban, Jeffrey E. (Chalmers University of Technology Steif, Christophe Garban, Jeffrey E. Steif


Kategori Diskret matematik


Sprog Engelsk


Indbinding Paperback


Sider 222


Udgave


Længde 13mm


Bredde 226mm


Højde 154mm


Udg. Dato 22 dec 2014


Oplagsdato 22 dec 2014

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