Behavior in groups of intermediate growth

Investigate multiple recurrence and L^2(μ) norm convergence for multiple ergodic averages when the acting group has intermediate (superpolynomial but subexponential) growth.

Background

While nilpotent actions support multiple recurrence and norm convergence, solvable groups of exponential growth can fail both properties.

The regime of intermediate growth (e.g., the Grigorchuk group) is presently poorly understood.