一類與Sierpinski地毯相關的擬可遷圖上的滲流模型.pdf

1、首都師范大學碩士學位論文一類與Sierpinski地毯相關的擬可遷圖上的滲流模型姓名：王彥申請學位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：吳憲遠20070408AbstractPercolationmodelwasfirstlyproposedbyBroadbentSRandHammerslyJMin1957，111isnotonlyextendstheresearchfieldsofprobabilitybutalsoprovide

2、sstrictb日目婦forstatPhysicsWeconsiderthepercolationonquasiitransitivegraphconnectedwithSierpinskiCarpetinthearticleInChapterI，wereviewthestudyprogr∞on80mepercolationmodelssuchasthepercolationonzdandsomelatticefractMsatfirs

3、tandweintroducetheSierpinskiCarpetThenwegivethestudyideainthisarticleAtlastwepresentthebasicdefinitionsandlemmawhichareusedinChapter2InChapter2，weUSetheenhancementtheorythesquareroottechnique，RSWlemma，ACCFRlemma，probabil

4、ityandme￡哪retostudythepercolationonquasitransitivegraphconnectedwithSierpinskiCarpetincludingcontinuityofthecriticalprobabilitytheuniquenessofinfiniteclustersandtheexponentialdecaysofennnectivityfunctionsandwegiveoutthes

5、trictprovementThenweprovethatthegraphswithdifierentisoperimetricdimensionscanhavethesamecriticalprobabilityKeyWords：percolation；SiepinfiskiCarpetlattice；Uniquenessofinfinitecluster；connectivity；criticalprobability；isoper