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Explore the mathematical concept of random walks on infinite graphs through this 46-minute conference talk that examines how to define random walk processes reflected upon reaching infinite ends of transient graphs. Learn about the application of this reflection process to study random planar maps in the universality class of supercritical Liouville quantum gravity (LQG) with central charge c in (1,25), which are characterized by being infinite with uncountably many ends. Discover the development of a version of the Tutte embedding for such maps that conjecturally converge to LQG, and examine phase transition conjectures for free uniform spanning forest and critical percolation based on the central charge of the model. Gain insights into advanced probability theory and mathematical physics through this research collaboration between Jinwoo Sung and Ewain Gwynne, presented at the Hausdorff Center for Mathematics.
