We provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.

中文翻译：

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具有稳定无限范围相互作用的吉布斯点过程的存在

基于熵水平的紧致性，我们提供了具有无限范围相互作用的吉布斯点过程存在的新证据。我们的主要存在定理在两个假设下成立。第一个是标准稳定性假设，这意味着任何有限配置的能量相对于点的数量都是超线性的。第二个假设是所谓的强度规律性，它通过过程的强度来控制相互作用的长程。这个假设是新的并在此引入，因为它很好地适应了熵方法。作为我们主要结果的推论，我们通过放宽超稳定性假设来改进 Ruelle (1970) 的成对相互作用的存在结果。