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The correct exponent for the Gotsman–Linial Conjecture

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Abstract

We prove new bounds on the average sensitivity of polynomial threshold functions. In particular, we show that for f, a degree-d polynomial threshold function in n variables that

$$\mathbb{AS}(f) \leq \sqrt{n}(\log(n))^{O(d log(d))}2^{O(d^2 log(d))}.$$

This bound amounts to a significant improvement over previous bounds, and in particular, for fixed d gives the same asymptotic exponent of n as the one predicted by the Gotsman–Linial Conjecture.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Building 380, Stanford, CA, 94305, USA

    Daniel M. Kane

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  1. Daniel M. Kane
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Correspondence to Daniel M. Kane.

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Kane, D.M. The correct exponent for the Gotsman–Linial Conjecture. comput. complex. 23, 151–175 (2014). https://doi.org/10.1007/s00037-014-0086-z

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  • DOI: https://doi.org/10.1007/s00037-014-0086-z

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