Abstract
We give a formula relating the L (2)-isoperimetric profile to the spectral distribution of a Laplace operator on a finitely generated group I". We prove the asymptotic stability of the spectral distribution under changes of measures with finite second moment. As a consequence, we can apply techniques from geometric group theory to estimate the spectral distribution of the Laplace operator in ...
Abstract
We give a formula relating the L (2)-isoperimetric profile to the spectral distribution of a Laplace operator on a finitely generated group I". We prove the asymptotic stability of the spectral distribution under changes of measures with finite second moment. As a consequence, we can apply techniques from geometric group theory to estimate the spectral distribution of the Laplace operator in terms of the growth and the Folner's function of the group. This leads to upper bounds on spectral distributions of some non-solvable amenable groups and to sharp estimates of the spectral distributions of some solvable groups with exponential growth.
Altmetric