平移不变性平均场系统的平衡态大偏差
Equilibrium large deviations for mean-field systems with translation invariance
摘要：
我们考虑具有平均场相互作用的粒子系统，其分布不受平移的影响。在假定从质心看系统关于Gibbs测度可逆的条件下，建立了平衡态下经验测度的大偏差原理。我们的研究涵盖了没有外部势的McKean-Vlasov粒子系统和基于秩的相互作用扩散系统的情况。根据相互作用的强度，大偏差原理在赋予适当阶的Wasserstein拓扑的中心概率测度空间中陈述，或者在平移对概率测度的作用的轨道空间中陈述。应用研究的非典型资本分配的详细说明。
英文摘要：
We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large deviation principles for its empirical measure at equilibrium. Our study covers the cases of McKean-Vlasov particle systems without external potential, and systems of rank-based interacting diffusions. Depending on the strength of the interaction, the large deviation principles are stated in the space of centered probability measures endowed with the Wasserstein topology of appropriate order, or in the orbit space of the action of translations on probability measures. An application to the study of atypical capital distribution is detailed.
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