Distributional and L-q norm inequalities for polynomials over convex bodies in R-n

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How researchers see this paper

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Efficient approaches for escaping higher order saddle points in non-convex optimization (2016, methodology): “We use the anti-concentration property for Gaussian random variables Theorem 14 (anti-concentration[Carbery and Wright, 2001]).”
Learning geometric concepts with nasty noise (2017, methodology): “However, since p is a normalized degree-2 polynomial, by standard anti-concentration bounds [CW01] we have that the probability that | p ( G ) | cα 4 is less than half the Gaussian mass of J , when c is sufﬁciently small.”
Anti-concentration for Polynomials of Independent Random Variables (2015, background): “Consider V. Vu is supported by NSF grant DMS-1307797 and AFORS grant FA9550-12-1-0083.”
Learning and Smoothed Analysis (2009, unknown): “This lemma is also a bit stronger than what holds for (non-multilinear) polynomials [3], [4] – here one can see that the polynomial x1 is too concentrated for our purposes.”
Learning Two-layer Neural Networks with Symmetric Inputs (2018, background): “Lemma 38 (Anti-concentration in Carbery and Wright (2001)).”