谢林斯分离模型的数学
对于那些不知道型号的人。您可以阅读此pdf。我想找出当算法收敛时（即当所有节点都满意时）2 个节点互为邻居的概率是多少。
这是该模型的要点。你有 一个网格（比如 10x10）。您有以下节点 两种（红色和绿色）各45。所以 我们有 10 个空位。我们随机 将节点放置在网格上。现在我们 扫描这个网格（精确顺序 没关系根据 谢林）。每个节点都需要一个特定的 同类人的百分比 其摩尔社区（假设 b = 50% 对于每个红色和绿色）。我们计算 每个节点的幸福度（a = Number 同类邻居数/数量 不同种类的邻居）。如果一个 节点不高兴（a < b）它移动到 它知道它所在的空单元格 快乐的。这个运动可以改变 新旧动态 邻里。算法收敛时 所有节点都很高兴。
PS - 我正在寻找谢林模型的任何数学分析的链接。
For those who don't know the model. You can read this pdf. I want to find what is the probability that 2 nodes are each others neighbors when the algorithm converges (i.e. when all nodes are happy).
Here's the model in a gist. You have
a grid (say 10x10). You have nodes of
two kind (red and green) 45 each. So
we have 10 empty spaces. We randomly
place the nodes on the grid. Now we
scan through this grid (Exact order
does not matter according to
Schelling). Each node wants a specific
percentage of people of same kind in
its Moore neighborhood (say b = 50%
for each red and green). We calculate
the happiness of each node (a = Number
of neighbors of same kind/Number of
neighbors of different kind). If a
node is unhappy (a < b) it moves to an
empty cell where it knows it will be
happy. This movement can change the
dynamics of old as well as new
neighborhood. Algorithm converges when
all nodes are happy.
PS - I am looking for links for any mathematical analysis of the Schelling's model.
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Easley 和 Kleinberg 所著的《网络、人群和市场：关于高度互联世界的推理》中对此模型进行了描述，请参阅 http://www.cs.cornell.edu/home/kleinber/networks-book/
这是一本非常好的书。
然而他们说：“最后一点，我们注意到，虽然该模型在数学上是精确且独立的，但讨论是在模拟和定性观察方面进行的。这是因为谢林模型的严格数学分析似乎是相当困难，并且在很大程度上是一个开放的研究问题。”他们确实参考了杨、莫比乌斯和罗森布拉特以及温科维奇和基尔曼的一些工作。
There is an account of this model in "Networks, Crowds, and Markets: Reasoning about a Highly Connected World", by Easley and Kleinberg, - see http://www.cs.cornell.edu/home/kleinber/networks-book/
This is a very good book.
However they say "As a final point, we note that while the model is mathematically precise and self-contained, the discussion has been carried out in terms of simulations and qualitative observations. This is because rigorous mathematical analysis of the Schelling model appears to be quite difficult, and is largely an open research question.." They do reference some work by Young, by Mobius and Rosenblat, and by Vinkovic and Kirman.