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Invariant and unimodular measures in the theory of random graphs

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Dealing with random infinite graphs inevitably leads to a study of invariance properties of the associated measures on the space of rooted graphs. In this context there are two natural notions: that of measures invariant with respect to the “root moving” equivalence relation (based on ideas from ergodic theory and geometry of foliations) and that of unimodular measures recently introduced by probabilists. I will give a brief survey of the area, and, in particular, clarify the relationship between these two classes of measures.

This talk is part of the Probability series.

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