arXiv subjects

Tobias Wassmer

Publications and source records attributed to Tobias Wassmer.

3 recordsLinked to original sources

arXiv2015

Aging of the Metropolis dynamics on the Random Energy Model

We study the Metropolis dynamics of the simplest mean-field spin glass model, the Random Energy Model. We show that this dynamics exhibits aging by showing that the properly rescaled time change process between the Metropolis dynamics and a suitably chosen `fast' Markov chain converges in distribution to a stable subordinator. The rescaling might depend on the realization of the environment, but we show that its exponential growth rate is deterministic.

math.PR↗

arXiv2014

Randomly trapped random walks on $\mathbb Z^d$

We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on $\mathbb Z^d$, $d\ge 2$. 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 $\mathbb Z^d$, this implies that the scaling limit of the randomly trapped random walk is either Brownian motion or the Fractional Kinetics process, as conjectured in [BCCR13].

math.PR↗

arXiv2013

Phase transition for the vacant set left by random walk on the giant component of a random graph

We study the simple random walk on the giant component of a supercritical Erdős-Rényi random graph on $n$ vertices, in particular the so-called vacant set at level $u$, the complement of the trajectory of the random walk run up to a time proportional to $u$ and $n$. We show that the component structure of the vacant set exhibits a phase transition at a critical parameter $u_{\star}$: For $u u_{\star}$ it has with high probability all components small. Moreover, we show that $u_{\star}$ coincides with the critical parameter of random interlacements on a Poisson-Galton-Watson tree, which was identified in [Tas10].

math.PR↗