  We define multidimensional tropical series, i.e. piecewise linear function
which are tropical polynomials locally but may have infinite number of
monomials. Tropical series appeared in the study of the growth of pluriharmonic
functions. However our motivation originated in sandpile models where certain
wave dynamic governs the behaviour of sand and exhibits a power law (so far
only experimental evidence). In this paper we lay background for tropical
series and corresponding tropical analytical hypersurfaces in the
multidimensional setting. The main object of study is $\Omega$-tropical series
where $\Omega$ is a compact convex domain which can be thought of the region of
convergence of such a series.
  Our main theorem is that the sandpile dynamic producing an $\Omega$-tropical
analytical hypersurface passing through a given finite number of points can
always be slightly perturbed such that the intermediate $\Omega$-tropical
analytical hypersurfaces have only mild singularities.
