{"title":"高维SOC的Curie-Weiss模型","authors":"M. Gorny","doi":"10.5802/AFST.1594","DOIUrl":null,"url":null,"abstract":"We build and study a multidimensional version of the Curie-Weiss model of self-organized criticality we have designed in arXiv:1301.6911. For symmetric distributions satisfying some integrability condition, we prove that the sum $S_n$ of the randoms vectors in the model has a typical critical behaviour. The fluctuations are of order $n^{3/4}$ and the limiting law has a density proportional to the exponential of a fourth-degree polynomial.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Curie-Weiss Model of SOC in Higher Dimension\",\"authors\":\"M. Gorny\",\"doi\":\"10.5802/AFST.1594\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We build and study a multidimensional version of the Curie-Weiss model of self-organized criticality we have designed in arXiv:1301.6911. For symmetric distributions satisfying some integrability condition, we prove that the sum $S_n$ of the randoms vectors in the model has a typical critical behaviour. The fluctuations are of order $n^{3/4}$ and the limiting law has a density proportional to the exponential of a fourth-degree polynomial.\",\"PeriodicalId\":122059,\"journal\":{\"name\":\"Annales de la faculté des sciences de Toulouse Mathématiques\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales de la faculté des sciences de Toulouse Mathématiques\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/AFST.1594\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de la faculté des sciences de Toulouse Mathématiques","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/AFST.1594","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We build and study a multidimensional version of the Curie-Weiss model of self-organized criticality we have designed in arXiv:1301.6911. For symmetric distributions satisfying some integrability condition, we prove that the sum $S_n$ of the randoms vectors in the model has a typical critical behaviour. The fluctuations are of order $n^{3/4}$ and the limiting law has a density proportional to the exponential of a fourth-degree polynomial.
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