  We study scaling limits of nonlinear functions $G$ of random grain model $X$
on $\mathbb{R}^d $ with long-range dependence and marginal Poisson
distribution. Following Kaj et al (2007) we assume that the intensity $M$ of
the underlying Poisson process of grains increases together with the scaling
parameter $\lambda$ as $M = \lambda^\gamma $, for some $\gamma > 0$. The
results are applicable to the Boolean model and exponential $G$ and rely on an
expansion of $G$ in Charlier polynomials and a generalization of Mehler's
formula. Application to solution of Burgers' equation with initial aggregated
random grain data is discussed.
