Markov duality and Bethe ansatz formula for half-line open ASEP
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916109439991808 |
|---|---|
| author | Barraquand, Guillaume Corwin, Ivan |
| author_facet | Barraquand, Guillaume Corwin, Ivan |
| contents | Using a Markov duality satisfied by ASEP on the integer line, we deduce a similar Markov duality for half-line open ASEP and open ASEP on a segment. This leads to closed systems of ODEs characterizing observables of the models. In the half-line case, we solve the system of ODEs using Bethe ansatz and prove an integral formula for $q$-moments of the current at $n$ distinct spatial locations. We then use this formula to confirm predictions for the moments of the multiplicative noise stochastic heat equation on $\mathbb R_{>0}$ with Robin type boundary condition and we obtain new formulas in the case of a Dirichlet boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07349 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Markov duality and Bethe ansatz formula for half-line open ASEP Barraquand, Guillaume Corwin, Ivan Probability Statistical Mechanics Mathematical Physics Using a Markov duality satisfied by ASEP on the integer line, we deduce a similar Markov duality for half-line open ASEP and open ASEP on a segment. This leads to closed systems of ODEs characterizing observables of the models. In the half-line case, we solve the system of ODEs using Bethe ansatz and prove an integral formula for $q$-moments of the current at $n$ distinct spatial locations. We then use this formula to confirm predictions for the moments of the multiplicative noise stochastic heat equation on $\mathbb R_{>0}$ with Robin type boundary condition and we obtain new formulas in the case of a Dirichlet boundary condition. |
| title | Markov duality and Bethe ansatz formula for half-line open ASEP |
| topic | Probability Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2212.07349 |