The polynomial Littlewood-Offord problem asks for anti-concentration inequality bounds for polynomials evaluated at
independent random signs. Let 
be a multilinear polynomial
of total degree 
with complex coefficients,
and let 
be the largest number of nonzero monomials
of total degree 
whose variable sets are pairwise disjoint. If 
are independent random signs, each taking the
values 
and 1 with probability 
,
then
 |
where 
is an absolute constant (Grebennikov 2026). For fixed 
,
the order 
is optimal.
Grebennikov (2026) attributes discovery of the argument to an autonomous GPT-6 Pro session and supplies a human-checked exposition of the proof.
