Interactions between Ehrenfest’s urns arising from group actions
Interactions between Ehrenfest’s urns arising from group actions
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群体行动引起的埃伦菲斯特瓮之间的相互作用
DOI：
10.1007/s11005-017-1043-y
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发表时间：
2018
影响因子：
1.2
通讯作者：
Mizukawa Hiroshi
中科院分区：
文献类型：
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作者：
平野幹;石井卓;宮崎直;Yoshinori Hamahata;佐藤文広;佐藤文広;Yoshinori Hamahata;佐藤文広;佐藤文広;Yoshinori Hamahata;Mizukawa Hiroshi
Escherichfest扩散模型是一个著名的经典物理模型，由两个瓮和两个球组成。Diaconis和Shahshahani使用Gelfand对模型进行了群论解释（Z Wahrsch Verw Gebiete 57（2）：159-179，1981）。这种解释对于anr-urns的推广仍然有效。则对应的Gelfand对为。然而，在这些模型中，对球的运动没有限制，即，每个球可以自由移动到任何一个骨灰盒。本文介绍了有限群作用引起的瓮之间的相互作用。球运动的自由度受有限群作用的限制。然后，我们表明，截止现象发生在一些特定的（但重要和有趣的）情况下。
The Ehrenfest diffusion model is a well-known classical physical model consisting of two urns andnballs. There is a group theoretical interpretation of the model by using the Gelfand pairby Diaconis and Shahshahani (Z Wahrsch Verw Gebiete 57(2):159–179, 1981). This interpretation is still valid for anr-urns generalization. Then the corresponding Gelfand pair is. However, in these models, there are no restrictions for ball movements, i.e., each ball can freely move to any urns. In this paper, interactions between urns arising from actions of finite groups are introduced. Degree of freedom of ball movements are restricted by finite group actions. We then show that the cutoff phenomenon occurs in some particular (yet significant and interesting) cases.