English

The Green function for waves on the $2$-regular Bethe lattice

Analysis of PDEs 2017-11-07 v1

Abstract

In this paper, we compute an explicit analytic expression for the Green function of the wave operator on the 22-regular lattice called the "Bethe lattice" equipped with its standard metric. In particular, we exhibit a phenomena of abnormal speed of propagation for waves: the effective speed of propagation of energy for large time is c=22/3<1c_*=2\sqrt 2/3 <1, and there exists a true propagation at any speed c<cc<c_*.

Cite

@article{arxiv.1711.01363,
  title  = {The Green function for waves on the $2$-regular Bethe lattice},
  author = {Kaïs Ammari and Gilles Lebeau},
  journal= {arXiv preprint arXiv:1711.01363},
  year   = {2017}
}
R2 v1 2026-06-22T22:35:50.077Z