Probability Seminar
Thursday, February 11, 2021, 3:15pm, Virtual
Jack Hanson (CCNY)
Bigeodesics and the density of the geodesic tree in first-passage percolation
In first-passage percolation, one assigns random nonnegative weights to the edges of Z^d and considers the resulting weighted graph metric. Many authors have studied the question of existence of "bigeodesics": doubly infinite geodesics for this metric, with most work in the case d = 2 (where bigeodesics have been ruled out in certain exactly solvable models). We will present the first progress on this question for d \geq 3 under no unproven assumptions. We will also discuss the resolution of the "highways and byways" conjecture of Hammersley-Welsh, showing in a sense that the density of points lying in geodesics containing the origin is zero.

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