  In this article we study asymptotic behavior of the probability that a random
monic polynomial with integer coefficients is irreducible over the integers. We
consider the cases where the coefficients grow together with the degree of the
random polynomials. Our main result is a generalization of a theorem proved by
Konyagin in 1999. We also generalize Hilbert's Irreducibility Theorem and
present an analog of this result with centered Binomial distributed
coefficients.
