eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-09-06
34:1
34:11
10.4230/LIPIcs.APPROX-RANDOM.2016.34
article
Lower Bounds on Same-Set Inner Product in Correlated Spaces
Hazla, Jan
Holenstein, Thomas
Mossel, Elchanan
Let P be a probability distribution over a finite alphabet Omega^L with all L marginals equal. Let X^(1), ..., X^(L), where X^(j) = (X_1^(j), ..., X_n^(j)) be random vectors such that for every coordinate i in [n] the tuples (X_i^(1), ..., X_i^(L)) are i.i.d. according to P.
The question we address is: does there exist a function c_P independent of n such that for every f: Omega^n -> [0, 1] with E[f(X^(1))] = m > 0 we have E[f(X^(1)) * ... * f(X^(n))] > c_P(m) > 0?
We settle the question for L=2 and when L>2 and P has bounded correlation smaller than 1.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol060-approx-random2016/LIPIcs.APPROX-RANDOM.2016.34/LIPIcs.APPROX-RANDOM.2016.34.pdf
same set hitting
product spaces
correlation
lower bounds