arXiv subjects

Spencer Durham

Publications and source records attributed to Spencer Durham.

2 recordsLinked to original sources

arXiv2026

A finite Livshits theorem and local length spectrum rigidity

We show that for closed negatively curved Riemannian manifolds whose length spectrum is exponentially separated, the length spectrum is a local isometry invariant. In particular, this holds for a dense set of negatively curved metrics. The main tool used in the proof is a finitary version of the Livshits theorem with an exponential tail.

math.DS↗

arXiv2026

On Rapid mixing for random walks on nilmanifolds

We prove rapid mixing for almost all random walks generated by $m$ translations on an arbitrary nilmanifold under mild assumptions on the size of $m$. For several classical classes of nilmanifolds, we show $m=2$ suffices. This provides a partial answer to the question raised in \cite{D02} about the prevalence of rapid mixing for random walks on homogeneous spaces.

math.DS↗