Extremal decomposition for random Gibbs measures: from general metastates to metastates on extremal random Gibbs measures

Electronic Communications in Probability

Codina Cotar¹ 

关键词: Gibbs measures;    disordered systems;    extremal decomposition;    metastates;   

DOI  :  10.1214/18-ECP200

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

The concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in the strong-coupling regime. We consider the general issue of the extremal decomposition for Gibbsian specifications which depend measurably on a parameter that may describe a whole random environment in the infinite volume. Given a random Gibbs measure, as a measurable map from the environment space, we prove measurability of its decomposition measure on pure states at fixed environment, with respect to the environment. As a general corollary we obtain that, for any metastate, there is an associated decomposition metastate, which is supported on the extremes for almost all environments, and which has the same barycenter.

【 授权许可】

CC BY