{"title":"随机介质中Z上随机游动的递归性","authors":"Julien Bremont","doi":"10.1016/S0764-4442(01)02173-5","DOIUrl":null,"url":null,"abstract":"<div><p>We study random walks on <span><math><mtext>Z</mtext></math></span> in a stationary random medium, defined by an ergodic dynamical system, when the possible jumps are {0,±1,±2}. We give a simple proof of a recurrence criterion of the same kind as Key's [6]. We show that the intermediate Lyapunov exponent involved in the criterion is always simple.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 1011-1016"},"PeriodicalIF":0.0000,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02173-5","citationCount":"4","resultStr":"{\"title\":\"On the recurrence of random walks on Z in random medium\",\"authors\":\"Julien Bremont\",\"doi\":\"10.1016/S0764-4442(01)02173-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study random walks on <span><math><mtext>Z</mtext></math></span> in a stationary random medium, defined by an ergodic dynamical system, when the possible jumps are {0,±1,±2}. We give a simple proof of a recurrence criterion of the same kind as Key's [6]. We show that the intermediate Lyapunov exponent involved in the criterion is always simple.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 11\",\"pages\":\"Pages 1011-1016\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02173-5\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021735\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021735","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the recurrence of random walks on Z in random medium
We study random walks on in a stationary random medium, defined by an ergodic dynamical system, when the possible jumps are {0,±1,±2}. We give a simple proof of a recurrence criterion of the same kind as Key's [6]. We show that the intermediate Lyapunov exponent involved in the criterion is always simple.
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