LONG RANGE RANDOM WALKS AND ASSOCIATED GEOMETRIES ON GROUPS OF POLYNOMIAL GROWTH

Zhen Qing Chen, Takashi Kumagai, Laurent Saloff-Coste, Jian Wang, Tianyi Zheng

研究成果: Article査読

1 被引用数 (Scopus)

抄録

In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study the large time behavior of its probability of return at time n in terms of the key parameters describing the driving measure and the structure of the underlying group. We obtain assorted estimates including near-diagonal two-sided estimates and the Hölder continuity of the solutions of the associated discrete parabolic difference equation. In each case, these estimates involve the construction of a geometry adapted to the walk.

本文言語English
ページ(範囲)1249-1304
ページ数56
ジャーナルAnnales de l'Institut Fourier
72
3
DOI
出版ステータスPublished - 2022
外部発表はい

ASJC Scopus subject areas

  • 代数と数論
  • 幾何学とトポロジー

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