Diffusive geodesics wandering in networks of rigid chains
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914179762356224 |
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| author | Marquis, Ulysse |
| author_facet | Marquis, Ulysse |
| contents | We introduce an ensemble of spatial networks built from the junctions of hindered-rotation chains, incorporating directional correlations between bonds, an aspect ignored in the standard network modeling paradigm. The emergent random networks support geodesics with a wandering exponent $ξ= 1/2$, and a travel-time fluctuation exponent $χ= 0$, consistent with the KPZ relation, yet violating the bound~$χ\geq1/8$ predicted in the Poissonian framework. Transverse deviations follow the Kolmogorov distribution, indicating similarities between Brownian bridge excursions and geodesics in a random medium with correlated edges orientations. These results reveal a new universality class of Euclidean first-passage percolation, where local orientational memory reshapes transport properties and challenges existing bounds for random spatial networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04682 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diffusive geodesics wandering in networks of rigid chains Marquis, Ulysse Disordered Systems and Neural Networks Statistical Mechanics Probability We introduce an ensemble of spatial networks built from the junctions of hindered-rotation chains, incorporating directional correlations between bonds, an aspect ignored in the standard network modeling paradigm. The emergent random networks support geodesics with a wandering exponent $ξ= 1/2$, and a travel-time fluctuation exponent $χ= 0$, consistent with the KPZ relation, yet violating the bound~$χ\geq1/8$ predicted in the Poissonian framework. Transverse deviations follow the Kolmogorov distribution, indicating similarities between Brownian bridge excursions and geodesics in a random medium with correlated edges orientations. These results reveal a new universality class of Euclidean first-passage percolation, where local orientational memory reshapes transport properties and challenges existing bounds for random spatial networks. |
| title | Diffusive geodesics wandering in networks of rigid chains |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2512.04682 |