Limit theorems for the nonattractive Domany-Kinzel model. 

作成者 香取, 眞理, 今野, 紀雄, 種村, 秀紀
作成者 (ヨミ) カトリ, マコト, タネムラ, ヒデキ
作成者の別表記 Katori, Makoto, Konno, Norio, Tanemura, Hideki
キーワード等 Domany-Kinzel model, nonattractive process, limit theorem, complete convergence theorem
日本十進分類法 (NDC) 417
内容 We study the Domany–Kinzel model, which is a class of discrete time Markov processes with two parameters $(p_1, p_2) \in [0,1]^2$ and whose states are subsets of $\mathbf{Z}$, the set of integers. When $p_1 = \alpha \beta$ and $p_2 = \alpha (2 \beta - \beta^2)$ with $(\alpha, \beta) \in [0,1]^2$, the process can be identified with the mixed site–bond oriented percolation model on a square lattice with the probabilities of open site a and of open bond $\beta$. For the attractive case, $0 \leq p_1 \leq p_2 \leq 1$, the complete convergence theorem is easily obtained. On the other hand, the case $(p_1, p_2) = (1,0)$ realizes the rule 90 cellular automaton of Wolframin which, starting from the Bernoulli measure with density $\theta$, the distribution converges weakly only if $\theta \in {0, 1/2, 1}$. Using our new construction of processes based on signed measures, we prove limit theorems which are also valid for nonattractive cases with $(p_1, p_2) \not= (1,0)$. In particular, when $p_2 \in [0,1]$ and $p_1$ is close to 1, the complete convergence theorem is obtained as a corollary of the limit theorems.
コンテンツの種類 雑誌掲載論文 Journal Article
DCMI資源タイプ text
ファイル形式 application/x-dvi
DOI 10.1214/aop/1023481012
掲載誌情報 The Annals of probability Vol.30 no.2 page.933-947 (2002)
言語 英語
関連情報 (hasVersion)
著者版フラグ author

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