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Explore the construction of multiple massive SLE(2) curves through this mathematical lecture that delves into the scaling limits of discrete curves. Learn about the foundational work of Makarov and Smirnov from 2009 on near-critical models and their scaling limits, with particular focus on the massive (or killed) random walk—a random walk process where there exists a probability of termination at each step. Discover how the loop-erasure of this process converges to the massive SLE(2) curve and examine the construction methodology that parallels the convergence of boundary branches of uniform spanning trees (UST) towards local multiple SLE(2). Investigate the absolute continuity properties of these mathematical objects and explore potential limit identification techniques using martingale observables, providing insights into advanced stochastic processes and their geometric interpretations.
