Rewriting History in Integrable Stochastic Particle Systems Article Swipe
Leonid Petrov
,
Axel Saenz
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.01643
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.01643
Many integrable stochastic particle systems in one space dimension (such as TASEP - Totally Asymmetric Simple Exclusion Process - and its $q$-deformation, the $q$-TASEP) remain integrable if we equip each particle with its own speed parameter. In this work, we present intertwining relations between Markov transition operators of particle systems which differ by a permutation of the speed parameters. These relations generalize our previous works (arXiv:1907.09155, arXiv:1912.06067), but here we employ a novel approach based on the Yang-Baxter equation for the higher spin stochastic six vertex model. Our intertwiners are Markov transition operators, which leads to interesting probabilistic consequences. First, we obtain a new Lax-type differential equation for the Markov transition semigroups of homogeneous, continuous-time versions of our particle systems. Our Lax equation encodes the time evolution of multipoint observables of the $q$-TASEP and TASEP in a unified way, which may be of interest for the asymptotic analysis of multipoint observables of these systems. Second, we show that our intertwining relations lead to couplings between probability measures on trajectories of particle systems which differ by a permutation of the speed parameters. The conditional distribution for such a coupling is realized as a "rewriting history" random walk which randomly resamples the trajectory of a particle in a chamber determined by the trajectories of the neighboring particles. As a byproduct, we construct a new coupling for standard Poisson processes on the positive real half-line with different rates.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2212.01643
- https://arxiv.org/pdf/2212.01643
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4310823551
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Raw OpenAlex JSON
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https://openalex.org/W4310823551Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2212.01643Digital Object Identifier
- Title
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Rewriting History in Integrable Stochastic Particle SystemsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-12-03Full publication date if available
- Authors
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Leonid Petrov, Axel SaenzList of authors in order
- Landing page
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https://arxiv.org/abs/2212.01643Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2212.01643Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2212.01643Direct OA link when available
- Concepts
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Integrable system, Particle system, Mathematics, Statistical physics, Observable, Markov chain, Markov process, Applied mathematics, Pure mathematics, Physics, Computer science, Quantum mechanics, Statistics, Operating systemTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.distribution | 183 |
| abstract_inverted_index.homogeneous, | 113 |
| abstract_inverted_index.intertwiners | 88 |
| abstract_inverted_index.intertwining | 41, 159 |
| abstract_inverted_index.trajectories | 168, 210 |
| abstract_inverted_index.consequences. | 98 |
| abstract_inverted_index.probabilistic | 97 |
| abstract_inverted_index.continuous-time | 114 |
| abstract_inverted_index.$q$-deformation, | 21 |
| abstract_inverted_index.(arXiv:1907.09155, | 65 |
| abstract_inverted_index.arXiv:1912.06067), | 66 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/10 |
| sustainable_development_goals[0].score | 0.8299999833106995 |
| sustainable_development_goals[0].display_name | Reduced inequalities |
| citation_normalized_percentile |