Model order reduction for the TASEP Master equation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929443537158144 |
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| author | Pioch, Kilian Kriecherbauer, Thomas Margaliot, Michael Grüne, Lars |
| author_facet | Pioch, Kilian Kriecherbauer, Thomas Margaliot, Michael Grüne, Lars |
| contents | The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional dynamics of interacting particles on a $1$D-lattice that is much used in systems biology and statistical physics. Its master equation describes the evolution of the probability distribution on the state space. The size of the master equation grows exponentially with the length of the lattice. It is known that the complexity of the system may be reduced using mean field approximations. We provide a rigorous derivation and a stochastic interpretation of these approximations and present numerical results on their accuracy for a number of relevant cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Model order reduction for the TASEP Master equation Pioch, Kilian Kriecherbauer, Thomas Margaliot, Michael Grüne, Lars Statistical Mechanics Optimization and Control Probability 34F05, 93A15 The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional dynamics of interacting particles on a $1$D-lattice that is much used in systems biology and statistical physics. Its master equation describes the evolution of the probability distribution on the state space. The size of the master equation grows exponentially with the length of the lattice. It is known that the complexity of the system may be reduced using mean field approximations. We provide a rigorous derivation and a stochastic interpretation of these approximations and present numerical results on their accuracy for a number of relevant cases. |
| title | Model order reduction for the TASEP Master equation |
| topic | Statistical Mechanics Optimization and Control Probability 34F05, 93A15 |
| url | https://arxiv.org/abs/2402.10234 |