Towards computing the Grothendieck constant
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Testing juntas nearly optimally
Proceedings of the forty-first annual ACM symposium on Theory of computing
Conditional hardness for satisfiable 3-CSPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
An invariance principle for polytopes
Proceedings of the forty-second ACM symposium on Theory of computing
On the inapproximability of vertex cover on k-partite k-uniform hypergraphs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Testing non-uniform k-wise independent distributions over product spaces
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Nearly optimal NP-hardness of vertex cover on k-uniform k-partite hypergraphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Beating the Random Ordering Is Hard: Every Ordering CSP Is Approximation Resistant
SIAM Journal on Computing
Bypassing UGC from some optimal geometric inapproximability results
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On LP-based approximability for strict CSPs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An invariance principle for polytopes
Journal of the ACM (JACM)
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We derive tight bounds on the expected value ofproducts of low influencefunctions defined on correlated probability spaces.The proofs are based on extending Fourier theory to an arbitrary number of correlatedprobability spaces, on a generalization of an invariance principlerecently obtained with O'Donnell andOleszkiewicz for multilinear polynomials withlow influences and bounded degree and on properties of multi-dimensionalGaussian distributions.Let $(X_i^j : 1 \leq i \leq k, 1 \leq j \leq n)$ be a matrix of random variables whose columns $X^1,\ldots,X^n$ are independent and identically distributed and such that any two rows $X_i, X_j$ for $1\leq i \neq j \leq k$ are independent.Assume further that the values that row $X_i$ takes with non-zero probability are the same no matter how one conditions on the remaining rows $X_1,\ldots,X_{i-1},X_{i+1},\ldots,X_k$.Our results show that given $k$ functions $f_1,\ldots,f_k$ taking values in $[0,1]$ it holds that $|\E[\prod_{i=1}^k f_i(X_i)] - \prod_{i=1}^k \E[f_i(X_i)]