二维随机游走回原点的概率
Two-Dimensional Random Walk
题目详情
Starting from an origin , a particle has a 50- 50 chance of moving 1 step north or 1 step south, and also a 50- 50 chance of moving 1 step east or 1 step west. After the step is taken, the move is repeated from the new position and so on indefinitely. What is the chance that the particle returns to the origin?
解析
二维对称随机游走是常返的（Pólya 定理）：以概率 1 会回到原点。
等价表述：回到原点的概率 为 1。