Spectral Dehn functions and a characterisation of word-hyperbolicity

Mayukh Mukherjee

We introduce a \emph{spectral Dehn function} \[ Λ_{\mathcal{P}}(n):=\inf λ_1(Δ), \] where ${\lambda }_1(\Delta )$ is the first Dirichlet eigenvalue of the random-walk Laplacian on a van Kampen di…