可逆Poisson-Kirchhoff系统
Reversible Poisson-Kirchhoff Systems
摘要：
本文定义了一类四分之一平面上水平和垂直加权折线随机系统，证明了其分布是平移不变的。这种不变性源于模型的可逆性。这类系统推广了同类的几个经典过程，如最后一次通过渗流理论中的Hammersley折线过程或某些特殊参数集的六顶点模型。新颖之处在于引入了与每条线相关联的权重。线最初产生的空间均匀加权泊松点过程和它们的演变（转向，分裂，交叉）是由马尔可夫动力学，保持基尔霍夫的节点定律的线的权重在每个路口。其中，我们得到了一些新的显式不变测度的一些子弹模型以及新的可逆性质的一些六顶点模型与外部电磁场。
英文摘要：
We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model. This class of systems generalizes several classical processes of the same kind, such as Hammersley's broken line processes involved in Last Passage Percolation theory or such as the six-vertex model for some special sets of parameters. The novelty comes here from the introduction of a weight associated with each line. The lines are initially generated by spatially homogeneous weighted Poisson Point Process and their evolution (turn, split, crossing) are ruled by a Markovian dynamics which preserves Kirchhoff's node law for the line weights at each intersection. Among others, we derive some new explicit invariant measures for some bullet models as well as new reversible properties for some six-vertex models with an external electromagnetic field.
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