We construct marked Gibbs point processes in $${\mathbb {R}}^d$$ R d under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an a.s. finite but random range. Secondly, the random marks—attached to the locations in $${\mathbb {R}}^d$$ R d —belong to a general normed space $${{\mathscr {S}}}$$ S . They are not bounded, but their law should admit a super-exponential moment. The approach used here relies on the so-called entropy method and large-deviation tools in order to prove tightness of a family of finite-volume Gibbs point processes. An application to infinite-dimensional interacting diffusions is also presented.

中文翻译：

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具有无界相互作用的标记吉布斯点过程：一个存在结果

我们在非常一般的假设下在 $${\mathbb {R}}^d$$ R d 中构造了标记的 Gibbs 点过程。首先，我们允许交互泛函可能是无界的，并且其范围不被假定为统一有界的。事实上，我们的典型交互承认有限但随机的范围。其次，随机标记 - 附加到 $${\mathbb {R}}^d$$ R d 中的位置 - 属于一般规范空间 $${{\mathscr {S}}}$$ S 。他们不受限制，但他们的法律应该承认一个超指数时刻。这里使用的方法依赖于所谓的熵方法和大偏差工具，以证明有限体积吉布斯点过程族的紧密性。还介绍了无限维相互作用扩散的应用。