Superdiffusive planar random walks with polynomial space-time drifts

Conrado da Costa; Mikhail Menshikov; Vadim Shcherbakov; Andrew Wade

doi:10.1016/j.spa.2024.104420

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arXiv · 2401.07813

Superdiffusive planar random walks with polynomial space-time drifts

Conrado da Costa·Mikhail Menshikov·Vadim Shcherbakov·Andrew Wade

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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.

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Conrado da Costa, Mikhail Menshikov, Vadim Shcherbakov, Andrew Wade. 2024-01-15. Superdiffusive planar random walks with polynomial space-time drifts. https://doi.org/10.1016/j.spa.2024.104420

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