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We study the problem of mass distribution of Laplacian eigenfunctions inshrinking balls for the standard flat torus$\mathbb{T}^2=\mathbb{R}^2/\mathbb{Z}^2$. By averaging over the centre of theball we use Bourgain's de-randomisation to compare the mass-distribution oftoral eigenfunctions at Plank scale to the mass distribution of random waves ingrowing balls around the origin. We are then able to classify all possiblelimiting distributions and variances. Finally we give sufficient and necessaryconditions so that the mass of \textquotedblleft generic \textquotedblrighteigenfunction equidistributes at Plank scale in almost all balls.

Mass distribution for toral eigenfunctions via Bourgain's de-randomisation