A random scatterers model for the Schrödinger operator on a free group (Q581931)

A model of rare scatterers was considered by \textit{A. G. Golitsyna} and \textit{S. A. Molchanov} [Dokl. Akad. Nauk SSSR 294, No.6, 1302-1306 (1987; Zbl 0662.60068)'' for a Schrödinger operator on an integer lattice \(Z^{\nu}\). In the framework of this model, both for \(Z_{\nu}\) and for a free group \(G_{\nu}\) it was possible to obtain a detailed description of the spectrum of the corresponding random Schrödinger operator. This paper utilizes the methods developed in the paper cited above and an explicit form of the Laplacian resolvent obtained Vestnik Moskov. Univ., Ser. I 26, No.4, 80-88 (1971; Zbl 0226.60082).