The seminar’s scope in broad revolves around theoretical physics and mathematics.

Seed Seminar of Mathematics and Physics

Unimodular Random Measured Metric Spaces and Palm Theory on Them

by Dr Ali Khezeli (Centre Inria de Paris, France and Tarbiat Modares University, Teheran, Iran.)

Europe/Paris
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Description

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