AI 中文总结
该研究证明有界度图上离散与连续时间的无限及有限碰撞性质分别等价，通过格林核比较等方法完成证明并关联对角无限访问。
AI 中文摘要
我们证明，在每一个连通有界度图上，离散时间下的无限碰撞性质成立当且仅常速连续时间下该性质成立，有限碰撞性质也存在相同等价关系。该证明基于同步离散时间对链与经泊松化得到的异步对链的格林核逐点比较，主要估计利用坐标更新的二项式交错及局部二项式估计，随后结合马丁容量与碰撞零一律，将该格林核比较与对角线上的无限访问关联起来。
英文摘要
We prove that, on every connected bounded-degree graph, the infinite collision property holds in discrete time if and only if it holds in constant-speed continuous time, and the same equivalence holds for the finite collision property. The proof is based on a pointwise comparison between the Green kernels of the synchronous discrete-time pair chain and the asynchronous pair chain obtained by Poissonization. The main estimate exploits the binomial interlacing of the coordinate updates together with a local binomial estimate. We then use Martin capacities and collision zero--one laws to relate this Green-kernel comparison to infinite visits of the diagonal.
