Consider the space $ S $ of homogeneous polynomials with rational coefficients of degree $ d $ in $ n $ variables. There are at most $\binom{n+d-1}{n} $ terms in the polynomial; for $ p \in S $, consider the `density of terms' of $ p $:
$$ \mu(p) = \frac{\text{number of terms in p}}{\binom{n+d-1}{n}} $$
Question: Is there a (qualitative or quantitative) correlation between $ \mu(p) $ and the irreducibility of $ p $ - i.e. in general, can one say something like `polynomials of fixed degree with higher $ \mu(p) $ are less likely to be reducible'? Is there any literature on this subject?
Bonus question: does it matter if we replace "irreducibility" with "absolute irreducibility"?
Somewhat related: Are most polynomials reducible or irreducible?
