Repository navigation
Add the monotone reduction and Russo's lemma for Boolean functions - #86
Merged
Merged
Conversation
Influence/Monotone.lean: every Boolean function on the hypercube can be replaced by a monotone one with the same expectation and no larger total influence (Theorem 9.10), via the shift operators and a maximal-potential argument. Influence/Threshold.lean: the p-biased hypercube, Russo's lemma d/dp E_p[f] = I^p(f) for monotone Boolean f (Theorem 9.15), and Corollary 9.16, I^p(f) <= sqrt(n E_p[f] / (p (1 - p))). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Add a References section to the Influence modules, prefix the numbered results with BLM, and drop labels that only made sense in the source notes. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Match the existing HDP citations, which use the abbreviation inline without a References section. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Influence/Monotone.lean: every Boolean function on the hypercube can be replaced by a monotone one with the same expectation and no larger total influence (Theorem 9.10), via the shift operators and a maximal-potential argument.
Influence/Threshold.lean: the p-biased hypercube, Russo's lemma d/dp E_p[f] = I^p(f) for monotone Boolean f (Theorem 9.15), and Corollary 9.16, I^p(f) <= sqrt(n E_p[f] / (p (1 - p))).
This PR corresponds to #85