Cotar, C;
Jahnel, B;
Kuelske, C;
(2018)
Extremal decomposition for random Gibbs measures: from general metastates to metastates on extremal random Gibbs measures.
Electronic Communications in Probability
, 23
, Article 95. 10.1214/18-ECP200.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | Extremal decomposition for random Gibbs measures: from general metastates to metastates on extremal random Gibbs measures |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/18-ECP200 |
| Publisher version: | https://doi.org/10.1214/18-ECP200 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Gibbs measures, disordered systems, extremal decomposition, metastates |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10064218 |
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