正则图上非回溯游走的生日悖论
The Birthday Paradox for non-backtracking walks on regular graphs
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中文总结 AI 辅助
该研究证明了正则图上度数≥3的随机非回溯游走存在生日悖论，即k远大于√n时高概率自相交，解决了Alon与Peres的固定度数猜想。
中文摘要 AI 辅助
我们针对度数至少为3的正则图上的随机非回溯游走，证明了一个生日悖论：当游走长度k显著大于√n时，这类游走以高概率发生自相交，其中n为图的顶点数。这解决了Noga Alon和Yuval Peres关于固定度数情形的一个猜想。
英文摘要
We show a birthday paradox for random non-backtracking walk on regular graphs of degree at least $3$: such a walk of length $k$ has high probability of self-intersecting when $k$ is significantly greater than $\sqrt n$, where $n$ is the number of vertices of the graph. This resolves a conjecture of Noga Alon and Yuval Peres for the fixed degree case.
