Superdiffusive planar random walks with polynomial space-time drifts

Fuente: arXiv
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Main Authors: da Costa, Conrado, Menshikov, Mikhail, Shcherbakov, Vadim, Wade, Andrew
Format: Preprint
Published: 2024
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author da Costa, Conrado
Menshikov, Mikhail
Shcherbakov, Vadim
Wade, Andrew
author_facet da Costa, Conrado
Menshikov, Mikhail
Shcherbakov, Vadim
Wade, Andrew
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2401_07813
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Superdiffusive planar random walks with polynomial space-time drifts
da Costa, Conrado
Menshikov, Mikhail
Shcherbakov, Vadim
Wade, Andrew
Probability
60J10 (Primary) 60G50, 60K50, 60F05, 60F15 (Secondary)
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.
title Superdiffusive planar random walks with polynomial space-time drifts
topic Probability
60J10 (Primary) 60G50, 60K50, 60F05, 60F15 (Secondary)
url https://arxiv.org/abs/2401.07813