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Invariance principle on the slice
- Publication Year :
- 2015
-
Abstract
- We prove an invariance principle for functions on a slice of the Boolean cube, which is the set of all vectors {0,1}^n with Hamming weight k. Our invariance principle shows that a low-degree, low-influence function has similar distributions on the slice, on the entire Boolean cube, and on Gaussian space. Our proof relies on a combination of ideas from analysis and probability, algebra and combinatorics. Our result imply a version of majority is stablest for functions on the slice, a version of Bourgain's tail bound, and a version of the Kindler-Safra theorem. As a corollary of the Kindler-Safra theorem, we prove a stability result of Wilson's theorem for t-intersecting families of sets, improving on a result of Friedgut.<br />Comment: 36 pages
- Subjects :
- Mathematics - Probability
Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1504.01689
- Document Type :
- Working Paper