Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916359952138240 |
|---|---|
| author | Halberstam, Noah Hutchcroft, Tom |
| author_facet | Halberstam, Noah Hutchcroft, Tom |
| contents | We compute the precise logarithmic corrections to Alexander-Orbach behaviour for various quantities describing the geometric and spectral properties of the four-dimensional uniform spanning tree. In particular, we prove that the volume of an intrinsic $n$-ball in the tree is $n^2 (\log n)^{-1/3+o(1)}$, that the typical intrinsic displacement of an $n$-step random walk is $n^{1/3} (\log n)^{1/9-o(1)}$, and that the $n$-step return probability of the walk decays as $n^{-2/3}(\log n)^{1/9-o(1)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01307 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree Halberstam, Noah Hutchcroft, Tom Probability Mathematical Physics We compute the precise logarithmic corrections to Alexander-Orbach behaviour for various quantities describing the geometric and spectral properties of the four-dimensional uniform spanning tree. In particular, we prove that the volume of an intrinsic $n$-ball in the tree is $n^2 (\log n)^{-1/3+o(1)}$, that the typical intrinsic displacement of an $n$-step random walk is $n^{1/3} (\log n)^{1/9-o(1)}$, and that the $n$-step return probability of the walk decays as $n^{-2/3}(\log n)^{1/9-o(1)}$. |
| title | Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2211.01307 |