Isbn: 9781107076433 - noise sensitivity of boolean functions and percolation (institute of mathematical statistics textbooks, 5, band 5) (10 Ergebnisse)

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Gebunden. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 sci.…

Zustand: New. PRINT ON DEMAND pp. 222.

Hardcover. Zustand: new. Hardcover. 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 SchrammLoewner 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. 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. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.…