Orthogonal Intertwiners for Infinite Particle Systems in The Continuum
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914672373923840 |
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| author | Wagner, Stefan |
| author_facet | Wagner, Stefan |
| contents | This article focuses on a system of sticky Brownian motions, also known as Howitt-Warren martingale problem, and correlated Brownian motions and shows that infinite-dimensional orthogonal polynomials intertwine the dynamics of infinitely many particles and their $n$-particle evolution. The proof is based on two assumptions about the model: information about the reversible measures for the $n$-particle dynamics and consistency. Additionally, explicit formulas for the polynomials are used, including a new explicit formula for infinite-dimensional Meixner polynomials, the orthogonal polynomials with respect to the Pascal process. As an application of the intertwining relations, new reversible measures for the infinite-particle dynamics are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03367 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Orthogonal Intertwiners for Infinite Particle Systems in The Continuum Wagner, Stefan Probability Mathematical Physics Functional Analysis 60J60, 60J25, 82C22 This article focuses on a system of sticky Brownian motions, also known as Howitt-Warren martingale problem, and correlated Brownian motions and shows that infinite-dimensional orthogonal polynomials intertwine the dynamics of infinitely many particles and their $n$-particle evolution. The proof is based on two assumptions about the model: information about the reversible measures for the $n$-particle dynamics and consistency. Additionally, explicit formulas for the polynomials are used, including a new explicit formula for infinite-dimensional Meixner polynomials, the orthogonal polynomials with respect to the Pascal process. As an application of the intertwining relations, new reversible measures for the infinite-particle dynamics are obtained. |
| title | Orthogonal Intertwiners for Infinite Particle Systems in The Continuum |
| topic | Probability Mathematical Physics Functional Analysis 60J60, 60J25, 82C22 |
| url | https://arxiv.org/abs/2305.03367 |