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Explore fundamental questions in statistical physics models on graphs through this 51-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 cutting-edge research in this field, including work on decorated planar maps based on collaborative research with Pablo Araya and Luis Fredes. Gain insights into the mathematical foundations that connect probability theory, graph theory, and statistical physics in this first part of a comprehensive mini-course series presented by the Hausdorff Center for Mathematics.
