Scaling, cumulant ratios and height distribution of the ballistic deposition in 3+1 and 4+1 dimensions

We investigate the origin of the scaling corrections in ballistic deposition models in high dimensions using the method proposed by Alves \textit{et al}. [Phys Rev. E \textbf{90}, 052405 (20014)] in $d=2+1$ dimensions, where the intrinsic width associated with the fluctuations of the height increments during the deposition processes is explicitly taken into account. In the present work, we show that this concept holds for $d=3+1$ and 4+1 dimensions. We have found that growth and roughness exponents and dimensionless cumulant ratios are in agreement with other models, presenting small finite-time corrections to the scaling, that in principle belong to the Kardar-Parisi-Zhang (KPZ) universality class in both $d=3+1$ and 4+1. Our results constitute a new evidence that the upper critical dimension of the KPZ class, if it exists, is larger than 4.