Consider a vertex-reinforced jump process defined on a regular tree, whereeach vertex has exactly $b$ children, with $b \ge 3$. We prove the strong lawof large numbers and the central limit theorem for the distance of the processfrom the root. Notice that it is still unknown if vertex-reinforced jumpprocess is transient on the binary tree.
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机译：考虑在规则树上定义的顶点增强的跳转过程，其中每个顶点正好有$ b $个子级，而$ b \ ge 3 $。我们证明了强大的大数定律和过程到根部距离的中心极限定理。注意，在二叉树上，顶点增强的跳转过程是否是瞬态的仍然是未知的。
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