While the zero-drift first arrival position (FAP) channel is known to exhibit a Cauchy noise distribution, practical molecular communication systems typically operate under nonzero drift. This letter analyzes the resulting transition in FAP noise behavior from heavy-tailed algebraic decay to exponential regularization. By asymptotically examining the exact FAP distribution, we identify a characteristic propagation distance (CPD) $r_c=σ^2/v$ that separates diffusion-dominated and drift-dominated regimes. Numerical results show that in low-drift environments, Gaussian approximations substantially underestimate the achievable rate, whereas the zero-drift Cauchy model provides a physically grounded performance baseline.

翻译：尽管零漂移首达位置信道已知呈现柯西噪声分布，实际分子通信系统通常在非零漂移下运行。本文分析了由此导致的FAP噪声行为从重尾代数衰减到指数正则化的转变。通过对精确FAP分布进行渐近分析，我们识别出区分扩散主导与漂移主导机制的特征传播距离$r_c=σ^2/v$。数值结果表明，在低漂移环境中，高斯近似会严重低估可达速率，而零漂移柯西模型提供了物理依据充分的性能基线。