Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree

M. T. Barlow, D. A. Croydon*, T. Kumagai

*この研究の対応する著者

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)57-111
ページ数55
ジャーナルProbability Theory and Related Fields
181
1-3
DOI
出版ステータスPublished - 2021 11月
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 統計学および確率
  • 統計学、確率および不確実性

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