On the spectral gap of Kawasaki dynamics under a mixing condition revisited
On the spectral gap of Kawasaki dynamics under a mixing condition revisited
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重温混合条件下川崎动力学的谱间隙
DOI：
10.1063/1.533192
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发表时间：
2000
影响因子：
1.3
通讯作者：
F. Martinelli
中科院分区：
文献类型：
--
作者：
N. Cancrini;F. Martinelli
我们考虑一个相对于晶格气体模型的正则吉布斯测度可逆的保守的随机自旋交换动力学。我们假定相应的大正则测度满足合适的强混合条件。我们从物理的角度给出了另一种很自然的证明，证明了著名的Lu-Yau结果，该结果表明，边L的盒子中的松弛时间像L2。然后，我们展示如何使用这样的估计来证明形式为1/tα - e的局部函数的衰减到平衡，其中e是正的并且任意小，对于d=1 α=12，对于d大于或等于2 α=1。
We consider a conservative stochastic spin exchange dynamics which is reversible with respect to the canonical Gibbs measure of a lattice gas model. We assume that the corresponding grand canonical measure satisfies a suitable strong mixing condition. We give an alternative and quite natural, from the physical point of view, proof of the famous Lu–Yau result which states that the relaxation time in a box of side L scales like L2. We then show how to use such an estimate to prove a decay to equilibrium for local functions of the form 1/tα−e, where e is positive and arbitrarily small and α=12 for d=1, α=1 for d⩾2.