Vortrag von 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.