Large deviations and law of large numbers for a mean field type interacting particle systems
Large deviations and law of large numbers for a mean field type interacting particle systems
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DOI：
10.1016/0304-4149(87)90199-2
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发表时间：
1987
影响因子：
1.4
通讯作者：
C. Léonard
中科院分区：
文献类型：
--
作者：
C. Léonard
在本文中，我们感兴趣的行为的经验措施的大交换系统N相互作用的粒子生活在波兰空间S，其法律在SN是吉布斯措施在0.1。当N趋于无穷大时，我们得到了经验测度的大偏差的Sanov型结果和一个弱大数定律。两者都处理相位共存的情况。当无限系统具有唯一相位时，得到了一个强大数定律。所有这些收敛都发生在概率测度的子空间中，其拓扑至少比通常的弱拓扑强。
In this paper, we are interested in the behaviour of the empirical measure of a large exchangeable system ofNinteracting particles living in a Polish spaceS, whose law inSNis the Gibbs measure given at 0.1. We get a Sanov type result for the large deviations of the empirical measure, and a weak law of large numbers, asNtends to infinity. Both handle the case of phase coexistence. A strong law of large numbers is obtained when the infinite system has a unique phase. All these convergences take place in a subspace of the probability measures whose topology is at least stronger than the usual weak one.