We study standard first-passage percolation via related optimization
problems that restrict path length. The path length variable is in duality with a shift of the weights. This puts into a convex duality framework old
observations about the convergence of geodesic length due to Hammersley,
Smythe and Wierman, and Kesten. We study the regularity of the time
constant as a function of the shift of weights. For unbounded weights,
this function is strictly concave and in case of two or more atoms it
has a dense set of singularities. For any weight distribution with an
atom at the origin there is a singularity at zero, generalizing a result of Steele and Zhang for Bernoulli FPP. The regularity results are proved by
the van den Berg-Kesten modification argument. This is joint work with
Arjun Krishnan and Timo Seppalainen
Probability and Combinatorics
Tuesday, October 2, 2018 - 3:00pm
Firas Rassoul-Agha
Utah