We extend a result of Freidlin and Gartner for KPP wave fronts to the case $d \geq 2$ for i.i.d. random media. We show a wave front propagation speed is attained for the discrete-space (lattice) KPP using a large deviation approach.
"Wave propagation in a lattice KPP equation in random media." Ann. Probab. 26 (3) 1179 - 1197, July 1998. https://doi.org/10.1214/aop/1022855748