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Explore the fundamental questions of statistical physics models on graphs through this mathematical lecture that examines which probability laws satisfy the Markov property and which random sets induce Markovian decompositions. Delve into three distinct settings: metric graphs, decorated random planar maps, and continuous domains, with particular focus on decorated planar maps based on recent research collaboration. Gain insights into advanced probability theory and statistical physics as applied to graph structures, building understanding of domain Markov properties and their mathematical foundations. Learn from cutting-edge research that bridges probability theory with geometric structures, offering both theoretical depth and practical applications in statistical physics modeling.
