Thursday, February 11, 2021, 3:15pm, Virtual

Jack Hanson (CCNY)

- 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.

Generated at 8:21am Sunday, April 18, 2021 by Mcal. Top * Reload * Login