论文标题
局部稀薄的随机场的吉布斯程度
Gibbsianness of locally thinned random fields
论文作者
论文摘要
我们考虑$ \ Mathbb Z^d $上的本地稀薄的Bernoulli字段，这是Euclidean Space中类型IMatérn铁杆过程的晶格版本。它作为职业变量的晶格字段，作为I.I.D的图像获得。在地图下，伯努利晶格场带有占用概率$ p $，在保留隔离粒子的同时，将所有粒子与邻居删除。我们证明，变薄的度量具有Gibbsian的代表性，并可以控制其准邻系依赖性，无论是在小$ p $的制度中，还是在大$ p $的制度中，在这里变薄的变化改变了伯努利的测量。我们的方法依赖于Dobrushin唯一性标准，分歧渗透论证和集群扩展。
We consider the locally thinned Bernoulli field on $\mathbb Z^d$, which is the lattice version of the Type-I Matérn hardcore process in Euclidean space. It is given as the lattice field of occupation variables, obtained as image of an i.i.d. Bernoulli lattice field with occupation probability $p$, under the map which removes all particles with neighbors, while keeping the isolated particles. We prove that the thinned measure has a Gibbsian representation and provide control on its quasilocal dependence, both in the regime of small $p$, but also in the regime of large $p$, where the thinning transformation changes the Bernoulli measure drastically. Our methods rely on Dobrushin uniqueness criteria, disagreement percolation arguments, and cluster expansions.
