Superdiffusive planar random walks with polynomial space-time drifts

• Main Authors: da Costa, Conrado, Menshikov, Mikhail, Shcherbakov, Vadim, Wade, Andrew
• Format: Journal Article
• Language: English
• Published: 25-06-2024
• Subjects: Mathematics - Probability
• DOI: 10.48550/arxiv.2401.07813

Stochastic Processes and their Applications, Vol. 176 (2024),
article 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.