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The Bethe ansatz for sticky Brownian motions
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Brockington, Dom and Warren, Jon (2023) The Bethe ansatz for sticky Brownian motions. Stochastic Processes and their Applications, 162 . pp. 1-48. doi:10.1016/j.spa.2023.04.015 ISSN 0304-4149.
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Official URL: http://doi.org/10.1016/j.spa.2023.04.015
Abstract
We consider a multi-dimensional diffusion whose coordinates behave as one-dimensional Brownian motions, evolving independently when apart, but with a sticky interaction when they coincide. We derive the Kolmogorov backwards equation and show that for a specific choice of interaction it can be solved exactly with the Bethe ansatz. The diffusion in
can be viewed as the
-point motions of a stochastic flow of kernels. We use our formulae to study the flow of kernels and show that atoms in the flow are asymptotically exponentially distributed in size at large times.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Brownian motion processes, Bethe-ansatz technique, Mathematical physics, Stochastic analysis | ||||||||
Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||
Publisher: | Elsevier Science BV | ||||||||
ISSN: | 0304-4149 | ||||||||
Official Date: | August 2023 | ||||||||
Dates: |
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Volume: | 162 | ||||||||
Page Range: | pp. 1-48 | ||||||||
DOI: | 10.1016/j.spa.2023.04.015 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 3 May 2023 | ||||||||
Date of first compliant Open Access: | 3 May 2023 | ||||||||
RIOXX Funder/Project Grant: |
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