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Explore the mathematical investigation of infinite clusters in probability theory through this 34-minute conference talk examining whether an infinite cluster exists when gluing two independent uniform noncrossing matchings. Delve into the connection between this simplified yet unsolved problem and the complex conjectures by Emmanuel and collaborators on meander enumeration. Learn about partial progress made on this question and discover related work on loop models on random quadrangulations. Gain insights into cutting-edge research in combinatorial probability theory and random geometry through collaborative findings with G. Kozma, L. Tournier, and V. Sidoravicius.
