On the Tail Transition of First Arrival Position Channels: From Cauchy to Exponential Decay
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915932759130112 |
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| author | Lee, Yen-Chi |
| author_facet | Lee, Yen-Chi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19074 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Tail Transition of First Arrival Position Channels: From Cauchy to Exponential Decay Lee, Yen-Chi Information Theory Signal Processing Probability 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. |
| title | On the Tail Transition of First Arrival Position Channels: From Cauchy to Exponential Decay |
| topic | Information Theory Signal Processing Probability |
| url | https://arxiv.org/abs/2511.19074 |