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Explore fundamental questions in statistical physics models on graphs through this 52-minute mathematical lecture that examines which probability laws satisfy the Markov property and which random sets induce Markovian decompositions. Delve into these concepts across three distinct settings: metric graphs, decorated random planar maps, and continuous domains. Learn about recent research developments in decorated planar maps based on collaborative work published in arXiv:2505.05447, providing insights into advanced topics at the intersection of probability theory, statistical physics, and graph theory.
