Lower bounds on same-set inner product in correlated spaces
Name
LIPIcs-APPROX-RANDOM-2016-34.pdf
Description
Published version
Size
505.8 KB
Format
Adobe PDF
Checksum (MD5)
23defe743159a94689498f81d915f5d0
Author(s)
Hazła, J
Holenstein, T
Mossel, E
Date Issued
September 1, 2016
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Citation
Lower Bounds on Same-Set Inner Product in Correlated Spaces. 19th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2016 and the 20th International Workshop on Randomization and Computation, RANDOM 2016, September 7, 2016 - September 9, 2016. 2016. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.
Version
Final published version
Abstract
Let Ρ be a probability distribution over a finite alphabet Ωℓ with all ℓ marginals equal. Let X(1), . . . , X(ℓ), X(j) = (X(j)1 , . . . , X(j)n ) be random vectors such that for every coordinate i ϵ [n] the tuples (X(i)1 , . . . , X(ℓ)i ) are i.i.d. according to Ρ. The question we address is: does there exist a function cΡ() independent of n such that for every f :Ωn → [0, 1] with E[f(X(1))] = μ > 0: E Φ Yj=1 f(X(j)) # ≥ cΡ(μ) > 0 ? We settle the question for ℓ = 2 and when ℓ > 2 and P has bounded correlation ρ(P) < 1.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2016.34
