Noise Sensitivity of Boolean Functions and Percolation

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.

Institute of Mathematical Stat Band 5

Noise Sensitivity of Boolean Functions and Percolation

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Beschreibung

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.

Christophe Garban is a CNRS researcher at UMPA, Ecole Normale Superieure, Lyon. Jeffrey Steif is a Professor of Mathematical Sciences at Chalmers University of Technology, Gothenburg, Sweden.

Details

  • Einband

    gebundene Ausgabe

  • Erscheinungsdatum

    31.12.2014

  • Verlag Cambridge
  • Seitenzahl

    222

Beschreibung

Details

  • Einband

    gebundene Ausgabe

  • Erscheinungsdatum

    31.12.2014

  • Verlag Cambridge
  • Seitenzahl

    222

  • Maße (L/B/H)

    23,1/15,2/1,8 cm

  • Gewicht

    431 g

  • Sprache

    Englisch

  • ISBN

    978-1-107-07643-3

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Die Leseprobe wird geladen.
  • Noise Sensitivity of Boolean Functions and Percolation
  • 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.