High dimensional behavior of the Kardar-Parisi-Zhang growth dynamics
  We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed non-perturbative renormalization for self-affine surface dynamics. Within this framework, we show that the roughness exponent $\alpha$ decays not faster than $\alpha\sim 1/d$ for large $d$. This implies the absence of a finite upper critical dimension. 
C. Castellano, A. Gabrielli, M. Marsili, M. A. Munoz and L. Pietronero