Claims

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1987_01_01_kashin: Proves that a random plus-minus one polynomial of degree n has minimum modulus on the unit circle at most the square root of n over the cube root of log n with probability tending to one; refereed, 1987.

1994_06_20_konyagin: Proves that a random plus-minus one polynomial of degree n has minimum modulus below n to the minus one half plus epsilon with probability tending to one, the first answer to the first question; refereed, 1994.

1999_08_27_konyagin_schlag: Proves that a random plus-minus one polynomial of degree n has minimum modulus below epsilon over root n with limiting probability at most a constant times epsilon, so the exponent minus one half is optimal.

2021_01_18_cook_nguyen: Proves that the minimum modulus of a random plus-minus one polynomial, scaled by the square root of the degree, has the same exponential limit law as in the Gaussian case, which contains the first question's answer.

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