论文标题
与高斯免费场有关的度量图上环汤的簇探索
Cluster explorations of the loop soup on a metric graph related to the Gaussian free field
论文作者
论文摘要
我们考虑以强度$ {1 \ over 2} $的循环汤，以当地时间$ 0 $在其效率上具有正职业的一组$ 0 $。我们在这种环状汤和在当地时代条件的通常的环汤之间提供关系。我们推定了werner证明的离散马尔可夫属性的循环汤的马尔可夫属性：探索群集时，群集外的桥梁形成了泊松点过程。我们展示了由于Le Jan而导致的物业有何关系，即环路汤的当地时代被分布成高斯自由田的正方形。最后，我们的结果自然会通过弗莱明（Fleming-Viot）过程在其职业领域中赋予循环汤的定律。 Werner通过随机电流模型以及Lupu，Sabot和Tarrès来解决这个问题的离散类似物。
We consider the loop soup at intensity ${1\over 2}$ conditioned on having local time $0$ on a set of vertices with positive occupation field in their vicinities. We give a relation between this loop soup and the usual loop soup conditioned on its local times. We deduce a domain Markov property for the loop soup, in the vein of the discrete Markov property proved by Werner: when exploring a cluster, the bridges outside the cluster form a Poisson point process. We show how it is related to the property due to Le Jan that the local times of the loop soup are distributed as the squares of a Gaussian free field. Finally, our results naturally give the law of the loop soup conditioned on its occupation field via Fleming--Viot processes. The discrete analog of this question was addressed by Werner in terms of the random current model, and by Lupu, Sabot and Tarrès by means of a self-interacting process.
