Dynamic ASEP, Duality, and Continuous q[superscript -1]-Hermite Polynomials
We demonstrate a Markov duality between the dynamic ASEP and the standard ASEP. We then apply this to step initial data, as well as a half-stationary initial data (which we introduce). While investigating the duality for half-stationary initial data, we uncover and utilize connections to continuo...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Oxford University Press (OUP)
2020
|
| Online Access: | https://hdl.handle.net/1721.1/123500 |
| _version_ | 1826203817117483008 |
|---|---|
| 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 demonstrate a Markov duality between the dynamic ASEP and the standard ASEP.
We then apply this to step initial data, as well as a half-stationary initial data (which we introduce).
While investigating the duality for half-stationary initial data, we uncover and utilize connections to
continuous q[superscript -1]-Hermite polynomials. Finally, we introduce a family of stationary initial data which
are related to the indeterminate moment problem associated with these q[superscript -1]-Hermite polynomials. |
| first_indexed | 2024-09-23T12:43:33Z |
| format | Article |
| id | mit-1721.1/123500 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:43:33Z |
| publishDate | 2020 |
| publisher | Oxford University Press (OUP) |
| record_format | dspace |
| spelling | mit-1721.1/1235002022-09-28T09:41:29Z Dynamic ASEP, Duality, and Continuous q[superscript -1]-Hermite Polynomials Borodin, Alexei Corwin, Ivan Massachusetts Institute of Technology. Department of Mathematics We demonstrate a Markov duality between the dynamic ASEP and the standard ASEP. We then apply this to step initial data, as well as a half-stationary initial data (which we introduce). While investigating the duality for half-stationary initial data, we uncover and utilize connections to continuous q[superscript -1]-Hermite polynomials. Finally, we introduce a family of stationary initial data which are related to the indeterminate moment problem associated with these q[superscript -1]-Hermite polynomials. National Science Foundation (U.S.) (Grant DMS-1056390) National Science Foundation (U.S.) (Grant DMS-1607901) 2020-01-21T20:07:52Z 2020-01-21T20:07:52Z 2018-01 2019-11-08T13:10:13Z Article http://purl.org/eprint/type/JournalArticle 1073-7928 1687-0247 https://hdl.handle.net/1721.1/123500 Borodin, Alexei and Ivan Corwin "Dynamic ASEP, Duality, and Continuous q−1-Hermite Polynomials." International Mathematics Research Notices (January 2018): rnx299 © The Author(s) 2018 en http://dx.doi.org/10.1093/imrn/rnx299 International Mathematics Research Notices Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press (OUP) arXiv |
| spellingShingle | Borodin, Alexei Corwin, Ivan Dynamic ASEP, Duality, and Continuous q[superscript -1]-Hermite Polynomials |
| title | Dynamic ASEP, Duality, and Continuous q[superscript -1]-Hermite Polynomials |
| title_full | Dynamic ASEP, Duality, and Continuous q[superscript -1]-Hermite Polynomials |
| title_fullStr | Dynamic ASEP, Duality, and Continuous q[superscript -1]-Hermite Polynomials |
| title_full_unstemmed | Dynamic ASEP, Duality, and Continuous q[superscript -1]-Hermite Polynomials |
| title_short | Dynamic ASEP, Duality, and Continuous q[superscript -1]-Hermite Polynomials |
| title_sort | dynamic asep duality and continuous q superscript 1 hermite polynomials |
| url | https://hdl.handle.net/1721.1/123500 |
| work_keys_str_mv | AT borodinalexei dynamicasepdualityandcontinuousqsuperscript1hermitepolynomials AT corwinivan dynamicasepdualityandcontinuousqsuperscript1hermitepolynomials |