Random walks on nilpotent groups driven by measures supported on powers of generators

  • Laurent Saloff-Coste

    Cornell University, Ithaca, United States
  • Tianyi Zheng

    Stanford University, USA

Abstract

We study the decay of convolution powers of a large family of measures on finitely generated nilpotent groups. Here, is a generating -tuple of group elements and is a -tuple of reals in the interval . The symmetric measure is supported by and gives probability proportional to to , . We determine the behavior of the probability of return as tends to infinity. This behavior depends in somewhat subtle ways on interactions between the -tuple and the positions of the generators within the lower central series , .

Cite this article

Laurent Saloff-Coste, Tianyi Zheng, Random walks on nilpotent groups driven by measures supported on powers of generators. Groups Geom. Dyn. 9 (2015), no. 4, pp. 1047–1129

DOI 10.4171/GGD/335