Mapping TASEP back in time
Mapping TASEP back in time
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DOI：
10.1007/s00440-021-01074-0
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发表时间：
2021-07
影响因子：
2
通讯作者：
L. Petrov;A. Saenz
中科院分区：
文献类型：
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作者：
L. Petrov;A. Saenz
从阶跃初始构型出发，得到了连续时间完全不对称简单不相容过程（TASEP）在不同时间的分布之间的新关系。也就是说，我们提出了一个具有局部相互作用和粒子依赖速率的连续时间马尔可夫过程，它在时间上向后映射TASEP分布。在反向过程中，粒子向左跳跃，动力学可以看作是离散空间哈默斯利过程的一个版本。结合前向TASEP进化，这导致了一个平稳的马尔可夫动力学保存，这反过来又带来了关于期望的新身份。后向动力学的构造基于Schur过程的马尔可夫映射交换参数，并由Yang-Baxter方程的对偶化驱动。我们还提出了一些推论，扩展，以及从我们的结构中产生的开放问题。
We obtain a new relation between the distributionsat different timesof the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributionsbackwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preservingwhich in turn brings new identities for expectations with respect to. The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.