- Series
- Stochastics Seminar
- Time
- Thursday, February 21, 2019 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Arjun Krishnan – University of Rochester – arjun.krishnan@rochester.edu – http://web.math.rochester.edu/people/faculty/akrish11/
- Organizer
- Michael Damron
Consider a measurable dense family of semi-infinite nearest-neighbor paths on the integer lattice in d dimensions. If the measure on the paths is translation invariant, we completely classify their collective behavior in d=2 under mild assumptions. We use our theory to classify the behavior of families of semi-infinite geodesics in first- and last-passage percolation that come from Busemann functions. For d>=2, we describe the behavior of bi-infinite trajectories, and show that they carry an invariant measure. We also construct several examples displaying unexpected behavior. One of these examples lets us answer a question of C. Hoffman's from 2016. (joint work with Jon Chaika)