Skip to main content

Research Repository

Advanced Search

Superdiffusive planar random walks with polynomial space–time drifts

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

Superdiffusive planar random walks with polynomial space–time drifts Thumbnail


Authors

Vadim Shcherbakov



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
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

Files





You might also like



Downloadable Citations