Non-existence of bi-infinite geodesics in the exponential corner growth model
Márton Balázs, Ofer Busani, Timo Seppäläinen
Abstract
Abstract This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.
Topics & Concepts
GeodesicMathematicsExponential functionPercolation (cognitive psychology)PlanarExponential growthPlanarity testingPercolation thresholdPure mathematicsMathematical analysisCombinatoricsExponentExponential map (Riemannian geometry)Property (philosophy)Exponential polynomialGrowth modelHomogeneousExponential decayGeometryZero (linguistics)Stochastic processes and statistical mechanicsRandom Matrices and ApplicationsTheoretical and Computational Physics