27/03/2024, 16:00 — 17:00 — Online
Alessandra Faggionato, University La Sapienza
An ergodic theorem with weights and applications to random measures, RW homogenisation and IPS hydrodynamics.
Birkhoff's ergodic theorem is a cornerstone in Mathematics, with a huge range of applications. We present here an extended form of the multidimensional ergodic theorem with weights, which allows to derive large scale averaging of stationary ergodic random measures on $\mathbb{R}^d$, also when the testing observables are not compactly supported. This control at infinity of random measures plays a crucial role when analysing the large scale behaviour of RWs and IPSs on weighted random graphs on $\mathbb{R}^d$ built on simple point processes. In particular, this allows us to obtain homogenization and hydrodynamics under weaker conditions.
We will then discuss several examples in order to emphasize the universality of our results.
