# Concentration of the number of solutions of random planted CSPs and Goldreich's one-way candidates

@article{Abbe2015ConcentrationOT, title={Concentration of the number of solutions of random planted CSPs and Goldreich's one-way candidates}, author={Emmanuel Abbe and Katherine Edwards}, journal={ArXiv}, year={2015}, volume={abs/1504.08316} }

This paper shows that the logarithm of the number of solutions of a random planted k-SAT formula concentrates around a deterministic n-independent threshold. Specically, if F k (;n ) is a random k-SAT formula on n variables, with clause density and with a uniformly drawn planted solution, there exists a function k( ) such that, besides for some in a set of Lesbegue measure zero, we have 1 logZ(F k (;n ))! k( ) in probability, where Z(F ) is the number of solutions of the formula F . This…

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