The goal of this paper is to prove that a random polynomial with independent and identically distributed random coefficients taking values uniformly in is irreducible with probability tending to as the degree tends to infinity. Moreover, we prove that the Galois group of the random polynomial contains the alternating group, again with probability tending to .
"Irreducible polynomials of bounded height." Duke Math. J. 169 (4) 579 - 598, 15 March 2020. https://doi.org/10.1215/00127094-2019-0047