abstracts for contributed talks

Yoshihiro Abe, Kyoto University

Title: Effective resistances for supercritical percolation clusters in boxes

Abstract: Consider supercritical bond percolation on the lattice. In this talk, I will describe a result on effective resistances for the largest open cluster in a box. I will apply this to estimating the cover time and the maximum of the Gaussian free field on the largest cluster. These results imply that there are quantitative differences between the cluster and the lattice in three or higher dimensional cases.

Erich Baur, ENS Lyon

Title: Exit laws of (an)isotropic random walks in random environment

Tomasz Tkocz, University of Warwick

Title: On some strange operators acting on L_1

Abstract: We shall discuss existence of bounded, linear operators acting on L_1[0,1] which are locally but not globally invertible (i.e. they are isomorphisms when restricted to the set of functions with small support, and yet they have infinite dimensional kernel). Joint work with Ball, Johnson, Nasseri and Schechtman.

Alex Tomberg, UBC

Title: Logarithmic corrections to scaling for the 4 dimensional weakly self-avoiding walk: watermelon networks

Abstract: We calculate the logarithmic correction to the decay of the critical two-point function for networks of p mutually-avoiding weakly self-avoiding walks joining two distant points on the 4-dimensional integer lattice. While similar results have been obtained previously for dimensions d > 4 by lace expansion, our proof is based on a rigorous renormalisation group analysis of a representation of the self-avoiding walk as a supersymmetric field theory. The talk is based on joint and ongoing work with Roland Bauerschmidt and Gordon Slade.

Florian Völlering, University of Göttingen

Title: Talagrand's inequality for Interacting Particle Systems

Abstract: Talagrand's inequality for independent Bernoulli random variables is extended to many interacting particle systems (IPS). The main assumption is that the IPS satisfies a log-Sobolev inequality. Additionally we also look at a common application, the relation between the probability of increasing events and the influences on that event by changing a single spin.

Tobias Wassmer, University of Vienna

Title: Randomly trapped random walks on Zd

Abstract: We give a complete classifi cation of scaling limits of randomly trapped random walks and associated clock processes on Zd, d\geq 2. Namely, under the hypothesis that the discrete skeleton of the randomly trapped random walk has a slowly varying return probability, we show that the scaling limit of its clock process is either deterministic linearly growing or a stable subordinator. In the case when the discrete skeleton is a simple random walk on Zd, this implies that the scaling limit of the randomly trapped random walk is either Brownian motion or the Fractional Kinetics process, as conjectured in [BCCR13].