Freeman, N. and Swart, J.M. (Submitted: 2025) Tightness criteria for random compact sets of cadlag paths. [Preprint - arXiv] (Submitted)
Abstract
We give tightness criteria for random variables taking values in the space of all compact sets of cadlag real-valued paths, in terms of both the Skorohod J1 and M1 topologies. This extends earlier work motivated by the study of the Brownian web that was concerned only with continuous paths. In the M1 case, we give a natural extension of our tightness criteria which ensures that non-crossing systems of paths have weak limit points that are also non-crossing. This last result is exemplified through a rescaling of heavy tailed Poisson trees and a more general application to weaves.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2025 The Author(s). This preprint is made available under a Creative Commons Attribution 4.0 International License. (https://creativecommons.org/licenses/by/4.0/) |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 24 Jan 2025 11:20 |
Last Modified: | 24 Jan 2025 11:20 |
Status: | Submitted |
Identification Number: | 10.48550/arXiv.2501.06930 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:222241 |