论文标题
多数选民的非可逆固定状态和树木上的动态
Non-reversible stationary states for majority voter and Ising dynamics on trees
论文作者
论文摘要
我们研究了在无限，无根的常规树上的三个马尔可夫过程：随机的ISING模型（也称为Ising模型的Glauber热浴动力学），多数选民动态和一个合并的粒子模型。在这三种情况下，树显示了编码在模型中的首选方向。对于所有三个模型，我们的主要结果是存在固定但不可逆的度量。对于ISING模型，这需要强加逆温度很大并选择合适的不均匀耦合，我们的定理意味着存在一种固定度量，看起来不像低温吉布斯的测量。我们结果的有趣方面在于，由于该图的不适应性，类似过程对$ \ mathbb z^d $没有非吉布斯的固定措施。实际上，迄今为止，尚无具有非可逆固定态的随机ising模型的例子。
We study three Markov processes on infinite, unrooted, regular trees: the stochastic Ising model (also known as the Glauber heat bath dynamics of the Ising model), a majority voter dynamic, and a coalescing particle model. In each of the three cases the tree exhibits a preferred direction encoded into the model. For all three models, our main result is the existence of a stationary but non-reversible measure. For the Ising model, this requires imposing that the inverse temperature is large and choosing suitable non-uniform couplings, and our theorem implies the existence of a stationary measure which looks nothing like a low-temperature Gibbs measure. The interesting aspect of our results lies in the fact that the analogous processes do not have non-Gibbsian stationary measures on $\mathbb Z^d$, owing to the amenability of that graph. In fact, no example of a stochastic Ising model with a non-reversible stationary state was known to date.
