Geometry of geodesics through Busemann measures in directed last-passage percolation

Firas Rassoul-Agha
University of Utah

We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and describe the geometry of the full set of semi-infinite geodesics in a typical realization of the random environment. The main tool is the Busemann functions viewed as a stochastic process indexed by the asymptotic direction. In the exactly solvable exponential model we give a complete characterization of the uniqueness and coalescence structure of the entire family of semi-infinite geodesics. Part of our results concerns the existence of exceptional (random) directions in which new interesting instability structures occur. Joint work with Christopher Janjigian and Timo Seppalainen.

Presentation (PDF File)

Back to Workshop IV: Stochastic Analysis Related to Hamilton-Jacobi PDEs