  Abelian differentials on Riemann surfaces can be seen as translation
surfaces, which are flat surfaces with cone-type singularities. Closed
geodesics for the associated flat metrics form cylinders whose number under a
given maximal length generically has quadratic asymptotics in this length, with
a common coefficient constant for the quadratic asymptotics called a
Siegel--Veech constant which is shared by almost all surfaces in each moduli
space of translation surfaces.
  Square-tiled surfaces are specific translation surfaces which have their own
quadratic asymptotics for the number of cylinders of closed geodesics. It is an
interesting question whether, as n tends to infinity, the Siegel--Veech
constants of square-tiled surfaces with n tiles tend to the generic constants
of the ambient moduli space. We prove that this is the case in the moduli space
H(2) of translation surfaces of genus two with one singularity.
