#### Kick-off event: Wednesday, November 6 afternoon at Institut Henri PoincarĂ©

Infos and registration: https://indico.math.cnrs.fr/e/NTQFTMR

# Unimodular Random Measured Metric Spaces and Palm Theory on Them

*by*

### Ali Khezeli

**Abstract:**

In this work, we define the notion of unimodular random measured metric spaces as a common generalization of various other notions. This includes the discrete cases like unimodular graphs and stationary point processes, as well as the non-discrete cases like stationary random measures and the continuum metric spaces arising as scaling limits of graphs. We provide various examples and prove many general results; e.g., on weak limits, re-rooting invariance, random walks, ergodic decomposition, amenability and balancing transport kernels. In addition, we generalize the Palm theory to point processes and random measures on a given unimodular space. This is useful for Palm calculations and also for reducing some problems to the discrete cases.

**Keywords:**

unimodular, mass transport principle, random metric space

All talks Fall '24: New trends in QFT, modularity, resurgence