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math.PR2018
Restricted percolation critical exponents in high dimensions
Shirshendu Chatterjee, Jack Hanson
Despite great progress in the study of critical percolation on for large, properties of critical clusters in high-dimensional fractional spaces and boxes remain…
math.PR2018
Lower bounds for fluctuations in first-passage percolation for general distributions
Michael Damron, Jack Hanson, Christian Houdré +1
In first-passage percolation (FPP), one assigns i.i.d.~weights to the edges of the cubic lattice and analyzes the induced weighted graph metric. If is the d…
math.PR2018
Infinite geodesics, asymptotic directions, and Busemann functions in first-passage percolation
Jack Hanson
We show existence, uniqueness, and directedness properties for infinite geodesics in the FPP model. After giving the fundamental definitions, we describe results by Newman and coll…