Sharp threshold result showing Θ(n²) random points in F_p^n pierce all algebraic sets defined by ≤s polynomials of degree ≤k, with application to random Szemerédi theorem.
On random multilinear operator inequalities
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abstract
It is a well known general principle that the Fourier transform of a random measure is small, except at the zero frequency, in various senses for appropriate notions of randomness. In this note we develop analogues of this principle for two classes of random multilinear operators. Two ergodic theoretic applications, involving correlations over randomly generated sparse subsequences, are obtained as corollaries of the main results.
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Randomly piercing algebraic sets
Sharp threshold result showing Θ(n²) random points in F_p^n pierce all algebraic sets defined by ≤s polynomials of degree ≤k, with application to random Szemerédi theorem.