Recurrence of random walks in the Ising spins |
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Authors: | Munemi Miyamoto |
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Institution: | 1. Yoshida College, Kyoto University, Kyoto, Japan
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Abstract: | Consider the 1/2-Ising model inZ 2. Let σ j be the spin at the site (j, 0)∈Z 2 (j=0, ±1, ±2, ...). Let \(\{ X_n \} _{n = 0}^{ + \infty } \) be a random walk with the random transition probabilities such that $$P(X_{n + 1} = j \pm 1|X_n = j) = p_j^ \pm \equiv 1/2 \pm v(\sigma _j - \mu )/2$$ We show a case whereEp j + ≧Ep j ? ], but \(\mathop {\lim }\limits_{n \to \infty } X_n = - \infty \) is recurrent a.s. |
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