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Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.

3 votes

Laplacian on manifolds and random matrix theory

This is somewhat different since the metrics are not generic, but there is a natural way to define the space of hyperbolic surfaces of a fixed genus. There has been a large amount of research studying …
Gabe K's user avatar
  • 6,001
3 votes

Time averages and differentiability

$\textbf{Update with some corrections}$: Unfortunately, my original answer had a serious gap. Sorry for the mix-up. The argument I gave only works when we have estimates on $A_T f(x)$ that are unifor …
Gabe K's user avatar
  • 6,001