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# The correct exponent for the Gotsman–Linial Conjecture

@article{Kane2013TheCE, title={The correct exponent for the Gotsman–Linial Conjecture}, author={Daniel M. Kane}, journal={2013 IEEE Conference on Computational Complexity}, year={2013}, pages={56-64} }

- Published 2013 in computational complexity
DOI:10.1007/s00037-014-0086-z

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 $$\mathbb{AS}(f) \leq \sqrt{n}(\log(n))^{O(d log(d))}2^{O(d^2 log(d))}.$$ AS ( f ) ≤ n ( log ( n ) ) O ( d l o g ( d ) ) 2 O ( d 2 l o g ( 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… CONTINUE READING

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