Superdiffusive planar random walks with polynomial space–time drifts

Conrado da Costa, Mikhail Menshikov, Vadim Shcherbakov and Andrew Wade

Stochastic Processes and their Applications, 2024, vol. 176, issue C

Abstract: 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.

Keywords: Random walk; Self-interaction; Excluded volume; Flory exponent; Anomalous diffusion (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104420

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