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- W1982371574 abstract "If f(x 1, …, x n ) is a polynomial dependent on a large number of independent Bernoulli random variables, what can be said about the maximum concentration of f on any single value? For linear polynomials, this reduces to one version of the classical Littlewood-Offord problem: Given nonzero constants a 1, …,a n , what is the maximum number of sums of the form ±a 1 ± a 2 ± … ± a n which take on any single value? Here we consider the case where f is either a bilinear form or a quadratic form. For the bilinear case, we show that the only forms having concentration significantly larger than n −1 are those which are in a certain sense very close to being degenerate. For the quadratic case, we show that no form having many nonzero coefficients has concentration significantly larger than n −1/2. In both cases the results are nearly tight." @default.
- W1982371574 created "2016-06-24" @default.
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- W1982371574 date "2012-06-29" @default.
- W1982371574 modified "2023-09-27" @default.
- W1982371574 title "Bilinear and quadratic variants on the Littlewood-Offord problem" @default.
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- W1982371574 doi "https://doi.org/10.1007/s11856-012-0082-4" @default.
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