A. Dawid

Random Hamiltonians II: A central limit theorem and the Hofer geometry of random walks

This paper investigates the global geometry of the group of Hamiltonian diffeomorphisms $\operatorname{Ham}(M,\omega)$ using random walks. On a large class of symplectic manifolds, we show that the expected Hofer norm of such a random walk grows at least as fast as the square root of the number of steps. Furthermore, w...