The 40th Midwest Probability Colloquium

Title: Shifted Weights and Restricted-Length Paths in First-Passage Percolation
Speaker: Firas Rassoul-Agha
Speaker Info: University of Utah
Brief Description:
Special Note:

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.
Date: Saturday, October 20, 2018
Time: 10:30am
Where: 107 Swift Hall
Contact Person: Elton Hsu
Contact email: ehsu!@math.northwestern.edu
Contact Phone: 18541
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