Bibliographic Details
| Title: |
Intertwinings for Continuum Particle Systems: an Algebraic Approach |
| Authors: |
Floreani, Simone, Jansen, Sabine, Wagner, Stefan |
| Source: |
SIGMA 20 (2024), 046, 21 pages |
| Publication Year: |
2023 |
| Collection: |
Mathematics
Mathematical Physics |
| Subject Terms: |
Mathematics - Probability, Mathematical Physics, Mathematics - Functional Analysis, 60J25, 60K35, 82C22, 22E60 |
| More Details: |
We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the $\mathfrak{su}(1,1)$ current algebra. We introduce raising, lowering, and neutral operators indexed by test functions and we use them to construct unitary operators, which act as self-intertwiners for some Markov processes having the Pascal process's law as a reversible measure. We show that such unitaries relate to generalized Meixner polynomials. Our primary results are continuum counterparts of results in the discrete setting obtained by Carinci, Franceschini, Giardin\`a, Groenevelt, and Redig (2019). |
| Document Type: |
Working Paper |
| DOI: |
10.3842/SIGMA.2024.046 |
| Access URL: |
http://arxiv.org/abs/2311.08763 |
| Accession Number: |
edsarx.2311.08763 |
| Database: |
arXiv |
