%0 Journal Article %1 barlow2011spectral %A Barlow, Martin T. %A Masson, Robert %D 2011 %J Comm. Math. Phys. %K fractal_dimension random_walk spectral_dimension uniform_spanning_tree %N 1 %P 23--57 %R 10.1007/s00220-011-1251-8 %T Spectral dimension and random walks on the two dimensional uniform spanning tree %U http://dx.doi.org/10.1007/s00220-011-1251-8 %V 305 %X We study the simple random walk on the uniform spanning tree on Z2 . We obtain estimates for the transition probabilities of the random walk, the distance of the walk from its starting point after n steps, and exit times of both Euclidean balls and balls in the intrinsic graph metric. In particular, we prove that the spectral dimension of the uniform spanning tree on Z2 is 16/13 almost surely. Obtains fractal dimension, walk dimension, and spectral dimension, which are related by Barlow, Coulhon, and Kumagai 2005.

@article{barlow2011spectral, abstract = {We study the simple random walk on the uniform spanning tree on Z2 . We obtain estimates for the transition probabilities of the random walk, the distance of the walk from its starting point after n steps, and exit times of both Euclidean balls and balls in the intrinsic graph metric. In particular, we prove that the spectral dimension of the uniform spanning tree on Z2 is 16/13 almost surely. Obtains fractal dimension, walk dimension, and spectral dimension, which are related by Barlow, Coulhon, and Kumagai 2005.}, added-at = {2013-11-10T00:43:42.000+0100}, author = {Barlow, Martin T. and Masson, Robert}, biburl = {https://www.bibsonomy.org/bibtex/28ffe9ab2a76541b5dcbfad218c7dfee7/peter.ralph}, coden = {CMPHAY}, doi = {10.1007/s00220-011-1251-8}, fjournal = {Communications in Mathematical Physics}, interhash = {9dcaa96cbb9467f0c456a7108e4a42f0}, intrahash = {8ffe9ab2a76541b5dcbfad218c7dfee7}, issn = {0010-3616}, journal = {Comm. Math. Phys.}, keywords = {fractal_dimension random_walk spectral_dimension uniform_spanning_tree}, mrclass = {60G50 (60C05)}, mrnumber = {2802298 (2012h:60145)}, mrreviewer = {Akira Sakai}, number = 1, pages = {23--57}, timestamp = {2013-11-10T00:43:42.000+0100}, title = {Spectral dimension and random walks on the two dimensional uniform spanning tree}, url = {http://dx.doi.org/10.1007/s00220-011-1251-8}, volume = 305, year = 2011 }