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Title: Last Passage Percolation And Its Scaling Limit Behaviour
Authors: R.T. Thiyageswaran, Vydhourie
Advisors: Dauvergne, Duncan
Department: Mathematics
Class Year: 2021
Abstract: The conjectured universal scaling limit in the KPZ universality class, including that of last passage percolation, is the directed landscape. We investigate the fluctuations of the directed landscape along its temporal and spatial coordinates separately. It is known that exponential and geometric last passage percolations demonstrate KPZ scaling exponents of 1/3 and 2/3 for their length and transversal fluctuations respectively, and the conjectured KPZ universal scaling relationship in dimension d = 2, where 2/3 = 2(1/3). We investigate this and related behaviours with paths/geodesics in last passage percolation in relation to their lengths/weights in the large-n regime.
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2021

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