Mean-field behaviour of the random connection model on hyperbolic space
- We study the random connection model on hyperbolic space H-d in dimension d=2,3. Vertices of the spatial random graph are given as a Poisson point process with intensity lambda>0. Upon variation of lambda, there is a percolation phase transition: there exists a critical value lambda(c)>0 such that for lambdalambda(c). We identify certain critical exponents that characterise the clusters at (and near) lambda(c), and show that they agree with the mean-field values for percolation. We derive the exponents through isoperimetric properties of critical percolation clusters rather than via a calculation of the triangle diagram.
| Author: | Matthew Dickson, Markus HeydenreichORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1269607 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/126960 |
| ISSN: | 0024-6107OPAC |
| ISSN: | 1469-7750OPAC |
| Parent Title (English): | Journal of the London Mathematical Society |
| Publisher: | Wiley |
| Place of publication: | Weinheim |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2025 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/12/10 |
| Volume: | 112 |
| Issue: | 5 |
| First Page: | e70345 |
| DOI: | https://doi.org/10.1112/jlms.70345 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung |
