Konferenz: Workshop on the occasion of Erwin Bolthausen's 70th birthday


Some properties of the membrane model

{{_Ltalk:R}} Prof. Dr. Rajat Subhra Hazra
Datum: 16.09.16   Zeit: 09.50 - 10.40   Raum: Y16G05

The membrane or bilaplacian model was first introduced in the physics literature to model random interfaces with constant curvature, and studied mathematically for the first time by Sakagawa and Kurt. It is a centered multivariate Gaussian whose covariance is given by the discrete bilaplacian operator on the lattice. It is tempting to think of it as a kin of the discrete Gaussian free field (GFF), and indeed many results can be deduced with the same methods for both, as for example while studying the fluctuations of the maximum in higher dimensions. Moreover as the GFF, it also can be seen as a generalised Gaussian variable arises as scaling limit of discrete models, for example in the odometer of the divisible sandpile or height fluctuations in uniform spanning forest. We will discuss some of these interesting features of the model. However, many techniques of the proofs need to be rethought of completely for this model, because of the lack of the random walk representation for its covariances. We will review some of these difficulties in our talk and explain how to handle them.

Based on joint works with Alberto Chiarini, Alessandra Cipriani and Wioletta Ruszel.