Researchers have established new bounds for the correlation gap under restricted independence, specifically addressing the case of n=4 and the worst-case scenario. For n=4, a universal 4/3 upper bound has been proven to hold, confirmed through a combination of theoretical analysis and AI-assisted computational verification. This proof involved techniques such as permutation symmetry, cone certificate systems, and recursive simplex subdivision. Additionally, the study demonstrates that the worst-case pairwise independent correlation gap can asymptotically reach $e/(e-1)$, matching the bound for mutual independence. This finding extends to t-wise independence for t>=2, indicating that pairwise independence can be as restrictive as mutual independence in certain situations. AI
IMPACT Establishes new theoretical bounds relevant to understanding the limitations of independence assumptions in complex systems.
RANK_REASON The cluster contains a research paper published on arXiv detailing new theoretical findings in mathematics and computer science. [lever_c_demoted from research: ic=1 ai=0.4]
- alphaXiv
- Arjun Ramachandran
- arXiv
- CatalyzeX
- cs.LG
- DagsHub
- Gotit.pub
- Hugging Face
- math.PR
- ScienceCast
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