In the present paper we show that for any given digraph , that is, an oriented graph without self-loops and 2-cycles, one can construct a 1-dependent Markov chain and n identically distributed hitting times T₁, … , T_n on this chain such that the probability of the event T_i > T_j, for any i, j = 1, … , n, is larger than if and only if . This result is related to various paradoxes in probability theory, concerning in particular non-transitive dice.

中文翻译：

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通过马尔可夫链的命中次数对图进行排序

在本文中，我们证明对于任何给定的有向图，即没有自环和 2 圈的有向图，可以构造一个依赖于 1 的马尔可夫链和n 个同分布的命中时间T ₁ , … ,  T _n on这个链使得事件T _i  >  T _j的概率，对于任何i，  j  = 1, … ,  n，大于当且仅当。这个结果与概率论中的各种悖论有关，特别是关于非传递骰子。