Speed of Convergence and Moderate Deviations of FPP on Random Geometric Graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915257537003520 |
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| author | de Lima, Lucas R. Valesin, Daniel |
| author_facet | de Lima, Lucas R. Valesin, Daniel |
| contents | This study delves into first-passage percolation on random geometric graphs in the supercritical regime, where the graphs exhibit a unique infinite connected component. We investigate properties such as geodesic paths, moderate deviations, and fluctuations, aiming to establish a quantitative shape theorem. Furthermore, we examine fluctuations in geodesic paths and characterize the properties of spanning trees and their semi-infinite paths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02046 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Speed of Convergence and Moderate Deviations of FPP on Random Geometric Graphs de Lima, Lucas R. Valesin, Daniel Probability Primary: 60K35, 82B43, 05C80, Secondary: 60C05, 60F10 This study delves into first-passage percolation on random geometric graphs in the supercritical regime, where the graphs exhibit a unique infinite connected component. We investigate properties such as geodesic paths, moderate deviations, and fluctuations, aiming to establish a quantitative shape theorem. Furthermore, we examine fluctuations in geodesic paths and characterize the properties of spanning trees and their semi-infinite paths. |
| title | Speed of Convergence and Moderate Deviations of FPP on Random Geometric Graphs |
| topic | Probability Primary: 60K35, 82B43, 05C80, Secondary: 60C05, 60F10 |
| url | https://arxiv.org/abs/2411.02046 |