环上的Toric tableaux与非齐次两种群TASEP
Toric tableaux and the inhomogeneous two-species TASEP on a ring
摘要：
环上的非均匀两种粒子TASEP是一个排它过程，它描述了不同种类的粒子在环上顺时针跳跃，参数给出了不同种类的跳跃率。我们引入一个组合对象，我们称之为\emph{toric rhombic alternative tableaux}，这是某些填充的tableaux上的三角形格子平铺菱形，并在双射与法拉利和马丁的研究\emph{multiline queues}。使用表格，我们得到一个公式的平稳概率，这TASEP，专门的Ayyer和Linusson的结果。此外，我们获得了一个明确的行列式公式，这些概率，并定义了一个马尔可夫链的tableaux项目的两个物种TASEP环上。
英文摘要：
The inhomogeneous two-species TASEP on a ring is an exclusion process that describes particles of different species hopping clockwise on a ring with parameters giving the hopping rates for different species. We introduce a combinatorial object that we call \emph{toric rhombic alternative tableaux}, which are certain fillings of tableaux on a triangular lattice tiled with rhombi, and are in bijection with the well-studied \emph{multiline queues} of Ferrari and Martin. Using the tableaux, we obtain a formula for the stationary probabilities of this TASEP, which specializes to results of Ayyer and Linusson. We obtain, in addition, an explicit determinantal formula for these probabilities, and define a Markov chain on the tableaux that projects to the two-species TASEP on a ring.
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