The true self-repelling motion. (English) Zbl 0912.60056

The paper presents a construction of the so-called true self-repelling motion that is a continuous counterpart of certain self-interacting random walks. Those true self-avoiding walks show-up a preference to propagate to areas which were less often visited in the past. In contract to the polymer-type self-avoiding walks, the true walk gives rise to a consistent family of probability measures. A continuous real-valued self-repelling process is Markovian, anomalous (enhanced, with the 3/2 scaling parameter) diffusion. The self-repulsion is due to the occupation-time measure density in the vicinity of a point that is just being visited. The multidimensional case is postponed to a future publication.


60G18 Self-similar stochastic processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
Full Text: DOI