Random Walks on Disordered Media and their Scaling Limits by Takashi Kumagai

Author:Takashi Kumagai
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(ii)Random walk on the two-dimensional uniform spanning tree [34]

It is proved that (5.​2) holds with D = 8∕5 and α = 1. Especially, it is shown that the spectral dimension of the random walk is 16∕13.

(iii)Brownian motion on the critical percolation cluster for the diamond lattice [131]

Brownian motion is constructed on the critical percolation cluster for the diamond lattice. Further, it is proved that the heat kernel enjoys continuous version of (5.​2) with α = 1 and some non-trivial D that is determined by the maximum eigenvalue of the matrix for the corresponding multi-dimensional branching process.

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