Large and moderate deviations in Poisson navigations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917398714515456 |
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| author | Ghosh, Partha Pratim Jahnel, Benedikt Jhawar, Sanjoy Kumar |
| author_facet | Ghosh, Partha Pratim Jahnel, Benedikt Jhawar, Sanjoy Kumar |
| contents | We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a Poisson point is joined by an edge to its nearest Poisson point to the right within a cone. We establish precise exponential rates of decay for the probability that the vertical displacement of the random path is unexpectedly large. The proofs rest on controlling the dependencies of the individual steps and the randomness in the horizontal displacement as well as renewal-process arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14295 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large and moderate deviations in Poisson navigations Ghosh, Partha Pratim Jahnel, Benedikt Jhawar, Sanjoy Kumar Probability 60D05, 60G70, 60G55, 05C80 We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a Poisson point is joined by an edge to its nearest Poisson point to the right within a cone. We establish precise exponential rates of decay for the probability that the vertical displacement of the random path is unexpectedly large. The proofs rest on controlling the dependencies of the individual steps and the randomness in the horizontal displacement as well as renewal-process arguments. |
| title | Large and moderate deviations in Poisson navigations |
| topic | Probability 60D05, 60G70, 60G55, 05C80 |
| url | https://arxiv.org/abs/2403.14295 |