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Explore the concept of noise stability beyond the traditional Boolean cube in this 59-minute lecture by Dan Mikulincer from MIT. Delve into the replacement of the standard heat semigroup with more general stochastic processes. Discover a new approach involving a re-normalized Brownian motion that embeds the discrete hypercube into the Wiener space. Examine the analysis of noise stability along its paths, leading to a novel quantitative form of the 'Majority is Stablest' theorem in Boolean analysis. Learn about the progress made on the 'most informative bit' conjecture by Courtade and Kumar. Gain insights into advanced mathematical concepts and their applications in information theory and Boolean analysis.
