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Random plane geometry – a gentle introduction
Random plane geometry – a gentle introduction
Consider Z^2, and assign a random length of 1 or 2 to each edge based on independent fair coin tosses. The resulting random geometry, first passage percolation, is conjectured to have a scaling limit. Most random plane geometric models (including hidden geometries) should behave the same. I will explain the basics of the limiting geometry, the "directed landscape", and its relation to traffic jams, tetris, coffee stains and random matrices.