Superdiffusive planar random walks with polynomial space-time drifts. (English) Zbl 07923187
Summary: We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is a polynomial function of the individual coordinates and of the present time. We describe how the model was motivated through an heuristic connection to a self-interacting, planar random walk which interacts with its own centre of mass via an excluded-volume mechanism, and is conjectured to be superdiffusive with a scale exponent \(3 / 4\). The self-interacting process originated in discussions with Francis Comets.
MSC:
| 60G50 | Sums of independent random variables; random walks |
| 60K50 | Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.) |
| 60F05 | Central limit and other weak theorems |
| 60F15 | Strong limit theorems |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
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