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Euclidean partitions optimizing noise stability

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Euclidean partitions optimizing noise stability
2.	Creator	Author's name, affiliation, country	Steven Heilman; Courant Institute NYU; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Standard simplex, plurality, optimization, MAX-k-CUT, Unique Games Conjecture
3.	Subject	Subject classification	68Q25
4.	Description	Abstract	The Standard Simplex Conjecture of Isaksson and Mossel asks for the partition $\{A_{i}\}_{i=1}^{k}$ of $\mathbb{R}^{n}$ into $k\leq n+1$ pieces of equal Gaussian measure of optimal noise stability.  That is, for $\rho>0$, we maximize$$\sum_{i=1}^{k}\int_{\mathbb{R}^{n}}\int_{\mathbb{R}^{n}}1_{A_{i}}(x)1_{A_{i}}(x\rho+y\sqrt{1-\rho^{2}})e^{-(x_{1}^{2}+\cdots+x_{n}^{2})/2}e^{-(y_{1}^{2}+\cdots+y_{n}^{2})/2}dxdy.$$Isaksson and Mossel guessed the best partition for this problem and proved some applications of their conjecture. For example, the Standard Simplex Conjecture implies the Plurality is Stablest Conjecture. For $k=3,n\geq2$ and $0<\rho<\rho_{0}(k,n)$, we prove the Standard Simplex Conjecture. The full conjecture has applications to theoretical computer science and to geometric multi-bubble problems (after Isaksson and Mossel).
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSF
7.	Date	(YYYY-MM-DD)	2014-08-15
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/3083
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-3083
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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