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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2511.16880 |
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| _version_ | 1866917398808887296 |
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| author | Chen, Xinxing Duquesne, Thomas Shi, Zhan |
| author_facet | Chen, Xinxing Duquesne, Thomas Shi, Zhan |
| contents | We study a class of random homogeneous systems. Our main result says that under suitable general assumptions, these systems converge weakly, upon a suitable normalization, to the probability distribution with density $\frac34 \, (1-x^2) \, {\bf 1}_{\{ x\in (-1, \, 1)\} }$. Two special cases are of particular interest: for the effective resistance of the critical random series-parallel graph, our result gives an affirmative answer to a conjecture of Hambly and Jordan (Adv. Appl. Probab. 2004) and further conjectures of Addario-Berry et al. (Probab.Theory Related Fields 2020) and Derrida whereas for the hipster random walk, we recover a previous result of Addario-Berry et al.~(Probab. Theory Related Fields 2020). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hipster random walks, random series-parallel graph and random homogeneous systems Chen, Xinxing Duquesne, Thomas Shi, Zhan Probability 60J80, 82B20, 82B27, 05C80 We study a class of random homogeneous systems. Our main result says that under suitable general assumptions, these systems converge weakly, upon a suitable normalization, to the probability distribution with density $\frac34 \, (1-x^2) \, {\bf 1}_{\{ x\in (-1, \, 1)\} }$. Two special cases are of particular interest: for the effective resistance of the critical random series-parallel graph, our result gives an affirmative answer to a conjecture of Hambly and Jordan (Adv. Appl. Probab. 2004) and further conjectures of Addario-Berry et al. (Probab.Theory Related Fields 2020) and Derrida whereas for the hipster random walk, we recover a previous result of Addario-Berry et al.~(Probab. Theory Related Fields 2020). |
| title | Hipster random walks, random series-parallel graph and random homogeneous systems |
| topic | Probability 60J80, 82B20, 82B27, 05C80 |
| url | https://arxiv.org/abs/2511.16880 |