@article{0b46b81f708741f69644d98ae71bc109,
title = "LONG RANGE RANDOM WALKS AND ASSOCIATED GEOMETRIES ON GROUPS OF POLYNOMIAL GROWTH",
abstract = "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 H{\"o}lder 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.",
keywords = "H{\"o}lder continuity, Pseudo-Poincar{\'e} inequality, group, long range random walk, return probability",
author = "Chen, {Zhen Qing} and Takashi Kumagai and Laurent Saloff-Coste and Jian Wang and Tianyi Zheng",
note = "Funding Information: Keywords: long range random walk, group, return probability, Pseudo-Poincar{\'e} inequality, H{\"o}lder continuity. 2020 Mathematics Subject Classification: 60G50, 20F65, 60B15. (*) The research of ZC is supported by Simons Foundation Grant 520542, a Victor Klee Faculty Fellowship at UW, and NNSFC grant 11731009, TK by the Grant-in-Aid for Scientific Research (A) 17H01093, Japan, LSC by NSF grants DMS-1404435 and DMS-1707589, and JW by NNSFC grant 11831014 and 12071076, and the Education and Research Support Program for Fujian Provincial Agencies. Publisher Copyright: {\textcopyright} 2022 Association des Annales de l'Institut Fourier. All rights reserved.",
year = "2022",
doi = "10.5802/aif.3515",
language = "English",
volume = "72",
pages = "1249--1304",
journal = "Annales de l'Institut Fourier",
issn = "0373-0956",
publisher = "Association des Annales de l'Institut Fourier",
number = "3",
}