- Stochastics Seminar
- Thursday, October 6, 2022 - 3:30pm for 1 hour (actually 50 minutes)
- Dan Mikulincer – MIT – Danmiku@gmail.com – https://www.wisdom.weizmann.ac.il/~danmi/
- Galyna Livshyts
Please Note: Recording: https://us02web.zoom.us/rec/share/cIdTfvS0tjar04MWv9ltWrVxAcmsUSFvDznprSBT285wc0VzURfB3X8jR0CpWIWQ.Sz557oNX3k5L1cpN
We revisit the notion of noise stability in the hypercube and show how one can replace the usual heat semigroup with more general stochastic processes. We will then introduce a re-normalized Brownian motion, embedding the discrete hypercube into the Wiener space, and analyze the noise stability along its paths. Our approach leads to a new quantitative form of the 'Majority is Stablest' theorem from Boolean analysis and to progress on the 'most informative bit' conjecture of Kumar and Courtade.