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This lecture explores the uniform dimer model from statistical mechanics, focusing on a near-critical weighted version and its connections to loop-erased random walks. Discover how the Temperley Bijection and Wilson's Algorithm link these mathematical structures to massive SLE_2, as constructed by Markarov and Smirnov. Follow along as Levi Haunschmid-Sibitz sketches the relationship between dimer models and loop-erased random walks, then delves into the properties of these walks and their scaling limits. Learn about the Girsanov identities that connect random walks with mass to random walks with drift, and examine the techniques and challenges involved in defining the continuum limit of these mathematical objects.
