Freeman, N. and Swart, J.M. (2024) Weaves, webs and flows. Electronic Journal of Probability, 29. pp. 1-82. ISSN 1083-6489
Abstract
We introduce weaves, which are random sets of non-crossing càdlàg paths that cover space-time R × R. The Brownian web is one example of a weave, but a key feature of our work is that we do not assume that the particle motions have any particular distribution. Rather, we present a general theory of the structure, characterization and weak convergence of weaves. We show that the space of weaves has an appealing geometry, involving a partition into equivalence classes under which each equivalence class contains a pair of dis-tinguished objects known as a web and a flow. Webs are natural generalizations of the Brownian web and the flows provide pathwise representations of stochastic flows. Moreover, there is a natural partial order on the space of weaves, characterizing the efficiency with which paths cover space-time, under which webs are precisely minimal weaves and flows are precisely maximal weaves. This structure is key to establishing weak convergence criteria for general weaves, based on weak convergence of finite collections of particle motions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Authors. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | weave; web; flow |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 21 Aug 2024 14:14 |
Last Modified: | 21 Aug 2024 14:14 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Refereed: | Yes |
Identification Number: | 10.1214/24-ejp1161 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:216231 |