<ul><li>The study of Kadar-Parsi-Zhang (KPZ) universality class and the coupling method in analyzing KPZ models has been of great interest.</li><li>In this study, the independence property of Busemann functions across multiple directions in various exactly solvable KPZ models is investigated.</li><li>The result shows that disjoint Busemann increments in different directions along a down-right path are independent, given that their associated semi-infinite geodesics have nonempty intersections.</li><li>Additionally, the existence of generalized Busemann functions and Gibbs measures for random walks in random potentials is established for a general class of lattice random walks in random potentials.</li></ul>

Working with Busemann functions part1(Machine Learning 2024)

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