# Mathematics Colloquia and Seminars

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### Robust Gaussian noise stability

Mathematical Physics & Probability

 Speaker: Joe Neeman, UC Berkeley Location: 1147 MSB Start time: Wed, Nov 7 2012, 4:10PM

Given two Gaussian vectors that are positively correlated, what is the probability that they both land in some fixed set A? Borell proved that this probability is maximized (over sets A with a given volume) when A is a half-space. We will give a new and simple proof of this fact, which also gives some stronger results. In particular, we can show that half-spaces uniquely maximize the probability above, and that sets which almost maximize this probability must be close to half-spaces.