论文标题
在有限量子组上随机步行的厄隆定理
The Ergodic Theorem for Random Walks on Finite Quantum Groups
论文作者
论文摘要
马尔可夫链具有雄性的必要条件是该链是不可还原且可观的。在有限组上随机行走的情况下，通过有关驾驶概率的支持的陈述来表现出来：有限组的随机步行在且仅当支持不集中在适当的子组上，或者是在适当的正常亚组的固定位置时。对有限组的随机步行的研究自然扩展到有限量子组的随机步行研究，在该量子组上，功能代数上的状态起驾驶概率的作用。在驾驶状态的支撑投影中给出了在有限量子组上随机行走的必要条件。
Necessary and sufficient conditions for a Markov chain to be ergodic are that the chain is irreducible and aperiodic. This result is manifest in the case of random walks on finite groups by a statement about the support of the driving probability: a random walk on a finite group is ergodic if and only if the support is not concentrated on a proper subgroup, nor on a coset of a proper normal subgroup. The study of random walks on finite groups extends naturally to the study of random walks on finite quantum groups, where a state on the algebra of functions plays the role of the driving probability. Necessary and sufficient conditions for ergodicity of a random walk on a finite quantum group are given on the support projection of the driving state.
