While the zero-drift first arrival position (FAP) channel exhibits a Cauchy-distributed lateral displacement, nonzero drift in practical systems introduces advective transport that regularizes this singular limit. This letter characterizes the drift-induced transition of FAP noise from heavy-tailed algebraic decay to exponential regularization. By asymptotically examining the exact FAP density, we identify a characteristic propagation distance (CPD) that serves as the fundamental boundary separating diffusion-dominated and drift-dominated regimes. Numerical evaluations demonstrate that in low-drift environments, variance-matched Gaussian approximations severely underestimate the true communication potential, whereas the zero-drift Cauchy law provides a robust, physically grounded performance baseline.

翻译：尽管零漂移首次到达位置信道呈现柯西分布的横向位移，实际系统中的非零漂移引入的对流输运会正则化这一奇异极限。本文刻画了漂移引起的FAP噪声从重尾代数衰减到指数正则化的转变过程。通过对精确FAP密度进行渐近分析，我们识别出特征传播距离这一基本边界，该边界分隔了扩散主导区与漂移主导区。数值评估表明：在低漂移环境中，方差匹配的高斯近似会严重低估实际通信潜力，而零漂移柯西定律则提供了稳健且物理依据充分的性能基准。