Abstract
Looptrees have recently arisen in the study of critical percolation on the uniform infinite planar triangulation. Here we consider random infinite looptrees defined as the local limit of the looptree associated with a critical Galton–Watson tree conditioned to be large. We study simple random walk on these infinite looptrees by means of providing estimates on volume and resistance growth. We prove that if the offspring distribution of the Galton–Watson process is in the domain of attraction of a stable distribution with index (Formula presented.) then the spectral dimension of the looptree is (Formula presented.).
Original language | English |
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Pages (from-to) | 1234-1261 |
Number of pages | 28 |
Journal | Journal of Statistical Physics |
Volume | 158 |
Issue number | 6 |
DOIs | |
Publication status | Published - Mar 2015 |
Bibliographical note
Funding Information:Research supported by the Knut and Alice Wallenberg Foundation.
Publisher Copyright:
© 2014, Springer Science+Business Media New York.
Other keywords
- Looptrees
- Random trees
- Random walk
- Spectral dimension