Central limit theorem for a random walk on Galton-Watson trees with random conductances
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910645405876224 |
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| author | Glatzel, Tabea Nagel, Jan |
| author_facet | Glatzel, Tabea Nagel, Jan |
| contents | We show a central limit theorem for random walk on a Galton-Watson tree, when the edges of the tree are assigned randomly uniformly elliptic conductances. When a positive fraction of edges is assigned a small conductance $\varepsilon$, we study the behavior of the limiting variance as $\varepsilon\to 0$. Provided that the tree formed by larger conductances is supercritical, the variance is nonvanishing as $\varepsilon\to 0$, which implies that the slowdown induced by the $\varepsilon$-edges is not too strong. The proof utilizes a specific regeneration structure, which leads to escape estimates uniform in $\varepsilon$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08768 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Central limit theorem for a random walk on Galton-Watson trees with random conductances Glatzel, Tabea Nagel, Jan Probability 60K37, 60F17, 60K40 We show a central limit theorem for random walk on a Galton-Watson tree, when the edges of the tree are assigned randomly uniformly elliptic conductances. When a positive fraction of edges is assigned a small conductance $\varepsilon$, we study the behavior of the limiting variance as $\varepsilon\to 0$. Provided that the tree formed by larger conductances is supercritical, the variance is nonvanishing as $\varepsilon\to 0$, which implies that the slowdown induced by the $\varepsilon$-edges is not too strong. The proof utilizes a specific regeneration structure, which leads to escape estimates uniform in $\varepsilon$. |
| title | Central limit theorem for a random walk on Galton-Watson trees with random conductances |
| topic | Probability 60K37, 60F17, 60K40 |
| url | https://arxiv.org/abs/2410.08768 |