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Random Walk on Random Infinite Looptrees

Jakob E. Björnberg (Institutionen för matematiska vetenskaper, matematisk statistik) ; S. O. Stefansson
Journal of statistical physics (0022-4715). Vol. 158 (2015), 6, p. 1234-1261.
[Artikel, refereegranskad vetenskaplig]

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 then the spectral dimension of the looptree is 2 alpha/(alpha+1).

Nyckelord: Looptrees, Random trees, Random walk, Spectral dimension

Denna post skapades 2015-04-16. Senast ändrad 2015-06-01.
CPL Pubid: 215275


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Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)



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