  The determination of the exact exponents of the KPZ class in any substrate
dimension $d$ is one of the most important open issues in Statistical Physics.
Based on the behavior of the dimensional variation of some exact exponent
differences for other growth equations, I find here that the KPZ growth
exponents (related to the temporal scaling of the fluctuations) are given by
$\beta_d = \frac{7}{8d+13}$. These exponents present an excellent agreement
with the most accurate estimates for them in the literature. Moreover, they are
confirmed here through extensive Monte Carlo simulations of discrete growth
models and real space renormalization group (RG) calculations for directed
polymers in random media (DPRM), up to $d=15$. The left-tail exponents of the
probability density functions for the DPRM energy provide another striking
verification of the analytical result above.

Statistical Mechanics