{"ID":2837539,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.19074","arxiv_id":"2511.19074","title":"On the Tail Transition of First Arrival Position Channels: From Cauchy to Exponential Decay","abstract":"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 distribution from heavy-tailed algebraic regime 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 experiments 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.","short_abstract":"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 distribution from heavy-tailed algebraic reg...","url_abs":"https://arxiv.org/abs/2511.19074","url_pdf":"https://arxiv.org/pdf/2511.19074v4","authors":"[\"Yen-Chi Lee\"]","published":"2025-11-24T13:10:43Z","proceeding":"cs.IT","tasks":"[\"cs.IT\",\"eess.SP\",\"math.PR\"]","methods":"[\"Diffusion Model\"]","has_code":false}