Superdiffusive planar random walks with polynomial space–time drifts

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

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.

Citation

da Costa, C., Menshikov, M., Shcherbakov, V., & Wade, A. (2024). Superdiffusive planar random walks with polynomial space–time drifts. Stochastic Processes and their Applications, 176, Article 104420. https://doi.org/10.1016/j.spa.2024.104420

• Journal Article Type: Article
• Acceptance Date: Jun 20, 2024
• Online Publication Date: Jun 28, 2024
• Publication Date: 2024-10
• Deposit Date: Jun 20, 2024
• Publicly Available Date: Jul 12, 2024
• Journal: Stochastic Processes and their Applications
• Print ISSN: 0304-4149
• Electronic ISSN: 1879-209X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 176
• Article Number: 104420
• DOI: https://doi.org/10.1016/j.spa.2024.104420
• Public URL: https://durham-repository.worktribe.com/output/2487640