分野別セミナー

Critical phenomena lie at the heart of modern probability, displaying
dramatic phase transitions and intricate structures. In this talk, I
will present an overview of critical percolation with two specific
examples. First, we investigate the anomalous random walk behavior of
level set percolation in Gaussian Free Field, showing how strong
correlations at the criticality give rise to distinctive diffusion
properties. Second, we examine last passage percolation under
heavy-tailed passage times, establishing how a power-law decay at the
critical exponent induces new scaling behaviors of optimal paths. These
two perspectives highlight the subtle interplay between geometry and
correlations at criticality, offering new insights into the structure of
random media.