Dimension Dependent Correlation Gap Bounds under Restricted Independence
The pairwise independent correlation gap is the ratio of the maximum expected value of a set function under arbitrary dependence to that under pairwise independence, measuring the loss from this independence restriction. Under mutual independence, this gap is universally bounded by $e/(e-1)$ for monotone submodular functions. With pairwise independence, a tighter $4/3$ upper bound was established for several special cases, including $n=3$, and conjectured to hold universally. A recent AI-assisted counterexample disproved this conjecture for $n=5$, leaving the validity of the $n=4$ bound and the tight worst case bound open. We resolve both questions. First, for $n=4$, we establish that the...
| Authors | Arjun Ramachandra |
|---|---|
| Primary category | math.PR |
| Published | 2 September 2026 |
| Last updated at source | 2 September 2026 |
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