Probability, Ergodic Theory, Mathematical Physics Seminar

On the Steele-Zhang conjecture in First-Passage Percolation

Arjun Krishnan

Friday, October 25th, 2019
3:00 PM - 4:00 PM
Hylan 1106 A

Abstract: We consider the time-constant of first-passage percolation in a given fixed direction as a function of a positive constant \(b\) added to the weights. The classical Hammersley-Welsh criterion relates the regularity of this function to the existence of a limiting geodesic length in a given direction. Steele and Zhang (2003) conjectured that this function is differentiable at all values \(b>0\) for Bernoulli weights. We disprove this conjecture.

Event contact: arjun dot krishnan at rochester dot edu