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Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics
AN ALMOST CONSTANT LOWER BOUND OF THE ISOPERIMETRIC COEFFICIENT IN THE KLS CONJECTURE
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Paper Summary
Paperzilla title
Slicing Through the KLS Conjecture: A Near-Constant Isoperimetric Bound!
This paper proves an almost constant lower bound for the isoperimetric coefficient in the KLS conjecture, improving upon previous bounds with better dimension dependency. This has implications for other related conjectures like Bourgain's slicing conjecture and the thin-shell conjecture, plus potential impacts on concentration inequalities and mixing time bounds for log-concave measures.
Possible Conflicts of Interest
None identified
Identified Weaknesses
Limited Practical Applicability
The paper focuses on highly theoretical mathematical concepts with limited practical application.
Difficult for Non-Experts
The paper's reliance on complex mathematical proofs makes it inaccessible to a wider audience.
Lack of Empirical Evidence
The paper doesn't offer concrete examples or simulations to demonstrate the implications of its findings.
Rating Explanation
The paper makes a significant theoretical contribution to the KLS conjecture by improving the lower bound. Though highly specialized, the rigorous mathematical approach and the potential implications for related conjectures warrant a strong rating.
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Original Title:
AN ALMOST CONSTANT LOWER BOUND OF THE ISOPERIMETRIC COEFFICIENT IN THE KLS CONJECTURE
File Name:
s00039-021-00558-4.pdf
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July 14, 2025 at 11:21 AM
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