Randomized box–ball systems, limit shape of rigged configurations and thermodynamic Bethe ansatz
We introduce a probability distribution on the set of states in a generalized box–ball system associated with Kirillov–Reshetikhin (KR) crystals of type An(1). Their conserved quantities induce n-tuple of random Young diagrams in the rigged configurations. We determine their limit shape as the syste...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2018-12-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S055032131830289X |
| _version_ | 1811280466456608768 |
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| author | Atsuo Kuniba Hanbaek Lyu Masato Okado |
| author_facet | Atsuo Kuniba Hanbaek Lyu Masato Okado |
| author_sort | Atsuo Kuniba |
| collection | DOAJ |
| description | We introduce a probability distribution on the set of states in a generalized box–ball system associated with Kirillov–Reshetikhin (KR) crystals of type An(1). Their conserved quantities induce n-tuple of random Young diagrams in the rigged configurations. We determine their limit shape as the system gets large by analyzing the Fermionic formula by thermodynamic Bethe ansatz. The result is expressed as a logarithmic derivative of a deformed character of the KR modules and agrees with the stationary local energy of the associated Markov process of carriers. |
| first_indexed | 2024-04-13T01:15:12Z |
| format | Article |
| id | doaj.art-3386d2ec98ed4c53a70ffe33ef454345 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-04-13T01:15:12Z |
| publishDate | 2018-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-3386d2ec98ed4c53a70ffe33ef4543452022-12-22T03:08:56ZengElsevierNuclear Physics B0550-32132018-12-01937240271Randomized box–ball systems, limit shape of rigged configurations and thermodynamic Bethe ansatzAtsuo Kuniba0Hanbaek Lyu1Masato Okado2Institute of Physics, University of Tokyo, Komaba, Tokyo 153-8902, Japan; Corresponding author.Department of Mathematics, University of California, Los Angeles, CA 90095, USADepartment of Mathematics, Osaka City University, Osaka, 558-8585, JapanWe introduce a probability distribution on the set of states in a generalized box–ball system associated with Kirillov–Reshetikhin (KR) crystals of type An(1). Their conserved quantities induce n-tuple of random Young diagrams in the rigged configurations. We determine their limit shape as the system gets large by analyzing the Fermionic formula by thermodynamic Bethe ansatz. The result is expressed as a logarithmic derivative of a deformed character of the KR modules and agrees with the stationary local energy of the associated Markov process of carriers.http://www.sciencedirect.com/science/article/pii/S055032131830289X |
| spellingShingle | Atsuo Kuniba Hanbaek Lyu Masato Okado Randomized box–ball systems, limit shape of rigged configurations and thermodynamic Bethe ansatz Nuclear Physics B |
| title | Randomized box–ball systems, limit shape of rigged configurations and thermodynamic Bethe ansatz |
| title_full | Randomized box–ball systems, limit shape of rigged configurations and thermodynamic Bethe ansatz |
| title_fullStr | Randomized box–ball systems, limit shape of rigged configurations and thermodynamic Bethe ansatz |
| title_full_unstemmed | Randomized box–ball systems, limit shape of rigged configurations and thermodynamic Bethe ansatz |
| title_short | Randomized box–ball systems, limit shape of rigged configurations and thermodynamic Bethe ansatz |
| title_sort | randomized box ball systems limit shape of rigged configurations and thermodynamic bethe ansatz |
| url | http://www.sciencedirect.com/science/article/pii/S055032131830289X |
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