Document

# Invariance Principle on the Slice

## File

LIPIcs.CCC.2016.15.pdf
• Filesize: 422 kB
• 10 pages

## Cite As

Yuval Filmus, Guy Kindler, Elchanan Mossel, and Karl Wimmer. Invariance Principle on the Slice. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 15:1-15:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.CCC.2016.15

## Abstract

We prove a non-linear invariance principle for the slice. As applications, we prove versions of Majority is Stablest, Bourgain's tail theorem, and the Kindler-Safra theorem for the slice. From the latter we deduce a stability version of the t-intersecting Erdos-Ko-Rado theorem.
##### Keywords
• analysis of boolean functions
• invariance principle
• Johnson association scheme
• the slice

## Metrics

• Access Statistics
• Total Accesses (updated on a weekly basis)
0

## References

1. Rudolf Ahlswede and Levon H. Khachatrian. The complete intersection theorem for systems of finite sets. Eur. J. Comb., 18(2):125-136, 1997.
2. Rudolf Ahlswede and Levon H. Khachatrian. A pushing-pulling method: New proofs of intersection theorems. Combinatorica, 19(1):1-15, 1999.
3. Roee David, Irit Dinur, Elazar Goldenberg, Guy Kindler, and Igor Shinkar. Direct sum testing. In ITCS 2015, 2015.
4. Charles F. Dunkl. A Krawtchouk polynomial addition theorem and wreath products of symmetric groups. Indiana Univ. Math. J., 25:335-358, 1976.
5. Charles F. Dunkl. Orthogonal functions on some permutation groups. In Relations between combinatorics and other parts of mathematics, volume 34 of Proc. Symp. Pure Math., pages 129-147, Providence, RI, 1979. Amer. Math. Soc.
6. Yuval Filmus. An orthogonal basis for functions over a slice of the boolean hypercube. Elec. J. Comb., 23(1):P1.23, 2016.
7. Ehud Friedgut. On the measure of intersecting families, uniqueness and stability. Combinatorica, 28(5):503-528, 2008. URL: http://dx.doi.org/10.1007/s00493-008-2318-9.
8. Subhash Khot. Inapproximability of NP-complete problems, discrete fourier analysis, and geometry. In Proceedings of the International Congress of Mathematicians, Hyderabad, India, 2010.
9. Guy Kindler, Naomi Kirshner, and Ryan O'Donnell. Gaussian noise sensitivity and Fourier tails, 2014. Manuscript.
10. Elchanan Mossel and Yuval Filmus. Harmonicity and invariance on slices of the Boolean cube. In 31st Conf. Comp. Comp., 2016.
11. Elchanan Mossel, Ryan O'Donnell, and Krzysztof Oleszkiewicz. Noise stability of functions with low influences: Invariance and optimality. Ann. Math., 171:295-341, 2010.
12. Richard M. Wilson. The exact bound in the Erdős-Ko-Rado theorem. Combinatorica, 4:247-257, 1984.