# 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.