  We formulate a version of the Random Wave Conjecture for the fourth moment of
Eisenstein series which is based on Zagier's regularized inner product. We
prove an asymptotic formula expressing the regularized fourth moment as a mean
value of L-functions. This is an advantage over previous work in the
literature, which has approached the fourth moment problem through truncated
Eisenstein series and not yielded a suitable expression in terms of
L-functions.
