##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability Seminar

## Steven Heilman

#### UCLA

## Low Correlation Noise Stability of Euclidean Sets

##### Abstract:

The noise stability of a Euclidean set is a well-studied quantity. This quantity uses the Ornstein-Uhlenbeck semigroup to generalize the Gaussian perimeter of a set. The noise stability of a set is large if two correlated Gaussian random vectors have a large probability of both being in the set. We will first survey old and new results for maximizing the noise stability of a set of fixed Gaussian measure. We will then discuss some recent results for maximizing the low-correlation noise stability of three sets of fixed Gaussian measures which partition Euclidean space. Finally, we discuss more recent results for maximizing the low-correlation noise stability of symmetric subsets of Euclidean space of fixed Gaussian measure. All of these problems are motivated by applications to theoretical computer science.

Host: Todd Kemp

### November 5, 2015

### 9:00 AM

### AP&M 6402

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