Abstract: We present a new proof of the BKT phase transition in the spin XY (planar rotor) model on any planar lattice — a result first established by Fröhlich and Spencer in 1981. Our approach is quite elementary. It does not go through the analysis of vortices but rather through the dual integer-valued height function. We use a recent result of Lammers on delcoalization of general height functions together with a new loop representation of spin correlations in the XY model, that we believe to be of independent interest.
This is joint work with Diederik van Engelenburg.
Abstract: The physical phenomenon of random surface growth can be captured by stochastic models which belong to the Kardar-Parisi-Zhang (KPZ) universality class. In the talk we introduce a typical example, the totally asymmetric simple exclusion process (TASEP). Its limiting fluctuations are known to be related to random matrix theory. We mention a few further related models in the universality class. Then we explain some details about the recent work with Patrik Ferrari about the upper tail decay of the limiting fluctuations of TASEP with random initial condition. The problem is related to the maximum of a Brownian motion with parabolic drift.
Abstract: I will discuss the large time behaviour of a Brownian diffusion in two dimensions, whose drift is divergence-free, ergodic and given by the curl of the 2-dimensional Gaussian Free Field. Together with G. Cannizzaro and L. Haundschmid, we prove the conjecture by B. Toth and B. Valko that the mean square displacement is of order $t \sqrt{\log t}$. The same type of superdiffusive behaviour has been predicted to occur for a wide variety of (self)-interacting diffusions in dimension d = 2: the diffusion of a tracer particle in a fluid, self-repelling polymers and random walks, Brownian particles in divergence-free random environments, and, more recently, the 2-dimensional critical Anisotropic KPZ equation. To the best of our authors’ knowledge, ours is the first instance in which $\sqrt{\log t}$ superdiffusion is rigorously established in this universality class.
After the seminar talks we will go out for dinner (going dutch) to some local restaurant. If you plan to join please do inform the local organizers (Gábor and/or Bálint) about this by Monday, 27th of September.
The Rényi Institute is in the very centre of the city. Trains from Vienna arrive at Keleti Station (rather central) with an earlier stop at Kelenföld Station (not so central). The RI is easily accessible from either of these using public transport . Kelenföld is further out, but time-wise it could be faster to get off the train there and take the metro/underground (M4) or the tram (49) as indicated below.
Here is how to come to the RI using public transport:
From Kelenföld Railway Station
Participants who wish to stay overnight in Budapest are kindly asked to make their own arrangements for accommodation.
Click here for hotels and hostels nearby the Rényi Institute (on Google maps).