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Intertwinings for general β -Laguerre and β -Jacobi processes
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Assiotis, Theodoros (2019) Intertwinings for general β -Laguerre and β -Jacobi processes. Journal of Theoretical Probability, 32 . pp. 1880-1891. doi:10.1007/s10959-018-0842-0 ISSN 0894-9840.
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Official URL: http://dx.doi.org/10.1007/s10959-018-0842-0
Abstract
We show that, for β≥1, the semigroups of β-Laguerre and β-Jacobi processes of different dimensions are intertwined in analogy to a similar result for β-Dyson Brownian motion recently obtained in Ramanan and Shkolnikov (Intertwinings of β-Dyson Brownian motions of different dimensions, 2016. arXiv:1608.01597). These intertwining relations generalize to arbitrary β≥1 the ones obtained for β=2 in Assiotis et al. (Interlacing diffusions, 2016. arXiv:1607.07182) between h-transformed Karlin–McGregor semigroups. Moreover, they form the key step toward constructing a multilevel process in a Gelfand–Tsetlin pattern leaving certain Gibbs measures invariant. Finally, as a by-product, we obtain a relation between general β-Jacobi ensembles of different dimensions.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Random matrices, Stationary processes, Semigroups | ||||||
| Journal or Publication Title: | Journal of Theoretical Probability | ||||||
| Publisher: | Springer New York LLC | ||||||
| ISSN: | 0894-9840 | ||||||
| Official Date: | December 2019 | ||||||
| Dates: |
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| Volume: | 32 | ||||||
| Page Range: | pp. 1880-1891 | ||||||
| DOI: | 10.1007/s10959-018-0842-0 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 17 September 2018 | ||||||
| Date of first compliant Open Access: | 18 September 2018 | ||||||
| RIOXX Funder/Project Grant: |
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