We propose a method for designing phased-arrays according to a given, analytically-specified, target beamshape. Building on the flexibeam framework, antenna locations are sampled from a probabilistic density function. Naturally scalable with the number of antennas, it is also computationally efficient and numerically stable, as it relies on analytical derivation. We prove that, under mild conditions, the achieved beamshapes converge uniformly to the target beamshapes as the number of antennas increases. We illustrate the technique through a number of examples. For instance, by use of the Laplace filter, beams with extremely fast decay away from the centre of focus are achieved. Some macroscopic observations result. We observe that matched beamforming weights may, for a given layout, achieve beamshapes targeting regions, rather than isolated directions as commonly believed. Additionally, the convergence analysis can be used to fore- cast the growth of future large phased arrays such as the Square Kilometre Array (SKA).