Discrete Time q-TASEPs
We introduce two new exactly solvable (stochastic) interacting particle systems which are discrete time versions of q-TASEP. We call these geometric and Bernoulli discrete time q-TASEP. We obtain concise formulas for expectations of a large enough class of observables of the systems to completely ch...
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| Format: | Article |
| Language: | en_US |
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Oxford University Press
2017
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| Online Access: | http://hdl.handle.net/1721.1/110552 https://orcid.org/0000-0002-2913-5238 |
| _version_ | 1826189379158147072 |
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| author | Borodin, Alexei Corwin, Ivan |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Corwin, Ivan |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | We introduce two new exactly solvable (stochastic) interacting particle systems which are discrete time versions of q-TASEP. We call these geometric and Bernoulli discrete time q-TASEP. We obtain concise formulas for expectations of a large enough class of observables of the systems to completely characterize their fixed time distributions when started from step initial condition. We then extract Fredholm determinant formulas for the marginal distribution of the location of any given particle.
Underlying this work is the fact that these expectations solve closed systems of difference equations which can be rewritten as free evolution equations with k−1 two-body boundary conditions—discrete q-deformed versions of the quantum delta Bose gas. These can be solved via a nested contour integral ansatz. The same solutions also arise in the study of Macdonald processes, and we show how the systems of equations our expectations solve are equivalent to certain commutation relations involving the Macdonald first difference operator. |
| first_indexed | 2024-09-23T08:13:48Z |
| format | Article |
| id | mit-1721.1/110552 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:13:48Z |
| publishDate | 2017 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | mit-1721.1/1105522022-09-23T11:48:20Z Discrete Time q-TASEPs Borodin, Alexei Corwin, Ivan Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Corwin, Ivan We introduce two new exactly solvable (stochastic) interacting particle systems which are discrete time versions of q-TASEP. We call these geometric and Bernoulli discrete time q-TASEP. We obtain concise formulas for expectations of a large enough class of observables of the systems to completely characterize their fixed time distributions when started from step initial condition. We then extract Fredholm determinant formulas for the marginal distribution of the location of any given particle. Underlying this work is the fact that these expectations solve closed systems of difference equations which can be rewritten as free evolution equations with k−1 two-body boundary conditions—discrete q-deformed versions of the quantum delta Bose gas. These can be solved via a nested contour integral ansatz. The same solutions also arise in the study of Macdonald processes, and we show how the systems of equations our expectations solve are equivalent to certain commutation relations involving the Macdonald first difference operator. National Science Foundation (U.S.) (Grant DMS-1056390) National Science Foundation (U.S.) (Grant DMS-1208998) Microsoft Research (Schramm Memorial Fellowship) Clay Mathematics Institute (Research Fellowship) 2017-07-07T18:20:56Z 2017-07-07T18:20:56Z 2013-10 2013-05 Article http://purl.org/eprint/type/JournalArticle 1073-7928 1687-0247 http://hdl.handle.net/1721.1/110552 Borodin, A., and I. Corwin. “Discrete Time Q-TASEPs.” International Mathematics Research Notices (2013): n. pag. https://orcid.org/0000-0002-2913-5238 en_US http://dx.doi.org/10.1093/imrn/rnt206 International Mathematics Research Notices Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press arXiv |
| spellingShingle | Borodin, Alexei Corwin, Ivan Discrete Time q-TASEPs |
| title | Discrete Time q-TASEPs |
| title_full | Discrete Time q-TASEPs |
| title_fullStr | Discrete Time q-TASEPs |
| title_full_unstemmed | Discrete Time q-TASEPs |
| title_short | Discrete Time q-TASEPs |
| title_sort | discrete time q taseps |
| url | http://hdl.handle.net/1721.1/110552 https://orcid.org/0000-0002-2913-5238 |
| work_keys_str_mv | AT borodinalexei discretetimeqtaseps AT corwinivan discretetimeqtaseps |