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ABSTRACT Modular nudging algorithms (inspired by Kalman filters) are presented.There are 3 main results. 1. If , analysis has implicit stability and explicit complexity:2. Forsmallandlarge, predictability horizons are infinite. 3. For any and , errors decrease and predictability horizons increase. Numerics confirm the method's effectiveness.
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On a problem of M. Talagrand
Abstract We address a special case of a conjecture of M. Talagrand relating two notions of “threshold” for an increasing family of subsets of a finite setV. The full conjecture implies equivalence of the “Fractional Expectation‐Threshold Conjecture,” due to Talagrand and recently proved by the authors and B. Narayanan, and the (stronger) “Expectation‐Threshold Conjecture” of the second author and G. Kalai. The conjecture under discussion here says there is a fixedLsuch that if, for a given , admits withand(a.k.a. isweakly p‐small), then admits such a taking values in ( is‐small). Talagrand showed this when is supported on singletons and suggested, as a more challenging test case, proving it when is supported on pairs. The present work provides such a proof.
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- PAR ID:
- 10521322
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Random Structures & Algorithms
- Volume:
- 61
- Issue:
- 4
- ISSN:
- 1042-9832
- Page Range / eLocation ID:
- 710 to 723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1002/rsa.21077
