### Road layout in the KPZ class (joint with Riddhipratim Basu, Sudeshna Bhattacharjee, Karambir Das, David Harper)

Probability Seminar

23rd February 2024, 3:30 pm – 4:30 pm

Fry Building, 2.04

In this talk I will be after a model for road layouts. Imagine a Poisson process on the plane for start points of cars. Each car picks an independent random direction and goes straight that way for some distance. I will start with showing that the origin (my house, that is) will see a lot of car traffic within an arbitrary small distance.

Which is not what we find in the real world out there, why? The answer is of course coalescence of paths in the random environment provided by hills and other geographic or societal obstacles. This points us towards first passage percolation (FPP), expected to be a member of the KPZ universality class. Due to lack of results for FPP, instead we built our model in exponential last passage percolation (LPP), known to be in the KPZ class. I will introduce LPP, then explain how to construct our road layout model in LPP, and what phenomena we can prove about roads and cars in this model using results from the LPP literature.

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