Superdiffusive planar random walks with polynomial space–time drifts

• Published in: Stochastic processes and their applications Vol. 176; p. 104420
• Main Authors: da Costa, Conrado, Menshikov, Mikhail, Shcherbakov, Vadim, Wade, Andrew
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-10-2024
• Subjects: Anomalous diffusion; Excluded volume; Flory exponent; Random walk; Self-interaction; secondary; Flory exponent; Excluded volume; Random walk; Self-interaction; Anomalous diffusion; primary
• ISSN: 0304-4149
• DOI: 10.1016/j.spa.2024.104420

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.