@article{1c4fe1c019874ae48fc40d18a864c81f,
title = "Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree",
abstract = "This article investigates the heat kernel of the two-dimensional uniform spanning tree. We improve previous work by demonstrating the occurrence of log-logarithmic fluctuations around the leading order polynomial behaviour for the on-diagonal part of the quenched heat kernel. In addition we give two-sided estimates for the averaged heat kernel, and we show that the exponents that appear in the off-diagonal parts of the quenched and averaged versions of the heat kernel differ. Finally, we derive various scaling limits for the heat kernel, the implications of which include enabling us to sharpen the known asymptotics regarding the on-diagonal part of the averaged heat kernel and the expected distance travelled by the associated simple random walk.",
keywords = "Heat kernel, Random walk, Uniform spanning tree",
author = "Barlow, {M. T.} and Croydon, {D. A.} and T. Kumagai",
note = "Funding Information: We thank Zhen-Qing Chen for asking us whether the elliptic Harnack inequalities hold for large scale in this model, which motivated us to work on Sect. , and for the analogy with reflecting Brownian motion in a planar domain with a slit removed given in Remark . This research was supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. Funding Information: M. T. Barlow: Research partially supported by NSERC (Canada). D. A. Croydon: Research partially supported by JSPS KAKENHI Grant Numbers 18H05832, 19K03540. T. Kumagai: Research partially supported by JSPS KAKENHI Grant Number JP17H01093 and by the Alexander von Humboldt Foundation. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2021",
month = nov,
doi = "10.1007/s00440-021-01078-w",
language = "English",
volume = "181",
pages = "57--111",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "1-3",
}