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arXiv · 1711.01363

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

Kaïs Ammari·Gilles Lebeau
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Abstract

In this paper, we compute an explicit analytic expression for the Green function of the wave operator on the $2$-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 $c_*=2\sqrt 2/3 <1$, and there exists a true propagation at any speed $c<c_*$.

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Kaïs Ammari, Gilles Lebeau. 2017-11-03. The Green function for waves on the $2$-regular Bethe lattice. https://arxiv.org/abs/1711.01363

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