Parameter Permutation Symmetry in Particle Systems and Random Polymers
نویسندگان
چکیده
Many integrable stochastic particle systems in one space dimension (such as TASEP - totally asymmetric simple exclusion process and its various deformations, with a notable exception of ASEP) remain when we equip each $x_i$ own jump rate parameter $\nu_i$. It is consequence integrability that the distribution $x_n(t)$ system started from step initial configuration depends on parameters $\nu_j$, $j\le n$, symmetric way. A transposition $\nu_n \leftrightarrow \nu_{n+1}$ thus affects only $x_n(t)$. For $q$-Hahn degenerations ($q$-TASEP directed beta polymer) realize an explicit Markov swap operator acting single polymer, can be interpreted modification lattice which polymer considered. Our main tools are duality contour integral formulas for joint moments. In particular, our constructions lead to continuous time $\mathsf{Q}^{(\mathsf{t})}$ preserving $\mathsf{t}$ $q$-TASEP (with configuration, where $\mathsf{t}\in \mathbb{R}_{>0}$ fixed). The dual certain transient $q$-Boson system. We identify asymptotic survival probabilities this $q$-moments $q$-TASEP, use show convergence arbitrary data stationary distribution. Setting $q=0$, recover results about usual established recently [arXiv:1907.09155] by different approach based Gibbs ensembles interlacing particles two dimensions.
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ژورنال
عنوان ژورنال: Symmetry Integrability and Geometry-methods and Applications
سال: 2021
ISSN: ['1815-0659']
DOI: https://doi.org/10.3842/sigma.2021.021