  We discuss the volume of Voronoi cells defined by two marked vertices picked
randomly at a fixed given mutual distance 2s in random planar quadrangulations.
We consider the regime where the mutual distance 2s is kept finite while the
total volume of the quadrangulation tends to infinity. In this regime, exactly
one of the Voronoi cells keeps a finite volume, which scales as s^4 for large
s. We analyze the universal probability distribution of this, properly
rescaled, finite volume and present an explicit formula for its Laplace
transform.
