| 广义自旋变相过程的不变测度集 |
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| 引用本文： | 任开隆.广义自旋变相过程的不变测度集[J].哈尔滨工程大学学报,1986(2). |
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| 作者姓名： | 任开隆 |
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| 作者单位： | 哈尔滨船舶工程学院数学教研室 |
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| 摘 要： | 关于无穷粒子系统不变测度的讨论已越来越引起人们的兴趣,R.A.Holley和D.W.Stroock在1]中给出了一维、二维随机Ising模型的不变测度都是GibbS态。唐守正在2]中给出了有界自旋变相过程在一定的条件下,它的不变测度也是Gibbs志。本文讨论了广义自旋变相过程(参见3]),当它是有界的或者其速度函数是强局部有限程的情况下,它的不变测度集与Gibbs态集重合,特别地若广义自旋变相过程有唯一的Gibbs态则一定遍历。
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| 关 键 词： | 自旋变相过程 不变测度 可逆测度 正测度 Gibbs态 有界过程 强局部有限程 位势 遍历性 |
The Invariant Measure Set for a Generalized Spin--flip Process |
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| Ren Kailong Teaching and Research section of Maths.The Invariant Measure Set for a Generalized Spin--flip Process[J].Journal of Harbin Engineering University,1986(2). |
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| Authors: | Ren Kailong Teaching and Research section of Maths |
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| Affiliation: | Ren Kailong Teaching and Research section of Maths |
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| Abstract: | R.A. Holley and D.W. Strock have given the fact that every stationarymeasure for a one or two dimensional stochastic Ising model is a Gibbsstate. Tang Shouzheng pointed out that under certain conditions theinvariant measure set for a bounded spin-flip process is also a Gibbs state set.this paper deals with the invariant measure set for a generalized spin-flipprocess, and shows that every invariant measure for a process which isbounded or the speed function of Which is of strongly local finite range isa Gibbs state. In particular if the potential has only one Gibbs state, thegeneralized spin-flip process must be ergodic. |
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| Keywords: | spin-flip process invariant measure reversible measure positive measure Gibbs state bounded process strongly local finite range potential ergodic |
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