Superdiffusive planar random walks with polynomial space-time drifts
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 coo...
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25-06-2024
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Shcherbakov, Vadim Menshikov, Mikhail da Costa, Conrado Wade, Andrew |
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| BackLink | https://doi.org/10.48550/arXiv.2401.07813$$DView paper in arXiv https://doi.org/10.1016/j.spa.2024.104420$$DView published paper (Access to full text may be restricted) |
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| Snippet | Stochastic Processes and their Applications, Vol. 176 (2024),
article 104420 We quantify superdiffusive transience for a two-dimensional random walk in
which... |
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| SubjectTerms | Mathematics - Probability |
| Title | Superdiffusive planar random walks with polynomial space-time drifts |
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