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Zbl 0912.60056
Tóth, Bálint; Werner, Wendelin
The true self-repelling motion. (English)
[J] Probab. Theory Relat. Fields 111, No.3, 375-452 (1998). ISSN 0178-8051; ISSN 1432-2064

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.
[Piotr Garbaczewski (Zielona Gora)]

MSC 2000:: *60G18 Self-similar processes
60K35 Interacting random processes
82C22 Interacting particle systems
82B41 Random walks, etc. (statistical mechanics)

Keywords: self-repelling motion; self-avoiding walk; stopping times; occupation-time; measure; polymer models

Cited in: Zbl 1110.65010 Zbl 1069.60068 Zbl 1101.82011 Zbl 0953.60027

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