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Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions

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タイトル: Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions
著者: Hofstad, Remco van der 著作を一覧する
Sakai, Akira 著作を一覧する
発行日: 2005年
出版者: Springer
誌名: Probability Theory and Related Fields
巻: 132
号: 3
開始ページ: 438
終了ページ: 470
出版社 DOI: 10.1007/s00440-004-0405-4
抄録: We consider self-avoiding walk and percolation in Zd , oriented percolation in Zd × Z+, and the contact process in Zd , with pD( · ) being the coupling function whose range is proportional to L. For percolation, for example, each bond is independently occupied with probabilitypD(y −x). The above models are known to exhibit a phase transition when the parameter p varies around a model-dependent critical point pc. We investigate the value of pc when d > 6 for percolation and d > 4 for the other models, and L 1. We prove in a unified way that pc = 1 + C(D) + O(L −2d ), where the universal term 1 is the mean-field critical value, and the model-dependent term C(D) = O(L −d ) is written explicitly in terms of the random walk transition probability D. We also use this result to prove that pc = 1 + cL −d + O(L −d−1), where c is a model-dependent constant. Our proof is based on the lace expansion for each of these models.
Rights: "The original publication is available at www.springerlink.com"
資料タイプ: article (author version)
URI: http://hdl.handle.net/2115/44916
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 坂井 哲

 

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