Random growth models and the KPZ universality

Many two-dimensional random growth models, including first- and last-passage percolation, are conjectured to fall within the KPZ universality class under mild assumptions on the underlying noise. In recent years, researchers have focused on a subset of exactly solvable models, where these conjectures can be rigorously verified. A wide array of methods has been employed, encompassing integrable probability, Gibbsian line ensemble, percolation arguments, and coupling techniques. This talk discusses a specific line of research that combines percolation arguments and coupling techniques to gain insights into the random geometry and space-time profiles of such growth models within the KPZ class.

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