Popov, Serguei; Vachkovskaia, Marina Random walk attracted by percolation clusters. (English) Zbl 1112.60089 Electron. Commun. Probab. 10, 263-272 (2005). Summary: Starting with a percolation model in \(\mathbb{Z}^d\) in the subcritical regime, we consider a random walk described as follows: the probability of transition from \(x\) to \(y\) is proportional to some function \(f\) of the size of the cluster of \(y\). This function is supposed to be increasing, so that the random walk is attracted by bigger clusters. For \(f(t)=e^{\beta t}\) we prove that there is a phase transition in \(\beta\), i.e., the random walk is subdiffusive for large \(\beta\) and is diffusive for small \(\beta\). Cited in 1 Document MSC: 60K37 Processes in random environments 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:subcritical percolation; subdiffusivity; reversibility; spectral gap PDFBibTeX XMLCite \textit{S. Popov} and \textit{M. Vachkovskaia}, Electron. Commun. Probab. 10, 263--272 (2005; Zbl 1112.60089) Full Text: DOI arXiv EuDML