Geometry and spectrum of rapidly branching graphs

Autoren: Matthias Keller, Felix Pogorzelski, Florentin Münch (2015)

We study graphs whose vertex degree tends and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth. The underlying techniques are estimates on the isoperimetric constant. Furthermore, we give lower volume growth bounds and we provide a new criterion for stochastic incompleteness.

Zeitschrift:
Mathematische Nachrichten
Seiten:
1636–1647
Band:
289

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