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arXiv · 1210.1283

The Correct Exponent for the Gotsman-Linial Conjecture

Daniel M. Kane
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Abstract

We prove a new bound on the average sensitivity of polynomial threshold functions. In particular we show that a polynomial threshold function of degree $d$ in at most $n$ variables has average sensitivity at most $\sqrt{n}(\log(n))^{O(d\log(d))}2^{O(d^2\log(d)}$. For fixed $d$ the exponent in terms of $n$ in this bound is known to be optimal. This bound makes significant progress towards the Gotsman-Linial Conjecture which would put the correct bound at $Θ(d\sqrt{n})$.

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Daniel M. Kane. 2012-10-04. The Correct Exponent for the Gotsman-Linial Conjecture. https://arxiv.org/abs/1210.1283

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