Abstract:
The directed landscape, L, is a random function on a 'directed' subset of R^4 that arises as the rescaled limit of last passage percolation. We sometimes think of it as a random 'metric' on R^2. We show that the level sets of last passage percolation converge to the level sets of the directed landscape in the Euclidean Hausdorff metric. We also describe the fractal nature of the level sets of the directed landscape. In particular, we prove that the level sets of L(0,0;0,t) have a Hausdorff dimension of 2/3 with positive probability and that the level sets of L(0,0;y,t) have a Hausdorff dimension of 5/3 also with positive probability. We prove this by finding matching upper and lower bounds. This is joint work with Lemonte Alie-Lamarche under supervision of Balint Virag. More details can be found in the following theses: https://tinyurl.com/
Biography:
Virginia Pedreira is a mathematician with interest in the area of probability. She received her PhD from the University of Toronto under the supervision of Balint Virag in September 2024. Before that, she was an undergraduate student at the University of Buenos Aires supervised by Pablo Groisman. Her research lies around the KPZ universality class with a focus on better understanding the directed landscape and the family of Tracy-Widom distributions.
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