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We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as boundary conditions for stationary last-passage percolation, define solutions to variational formulas that characterize limit shapes, and yield new results for Busemann functions, geodesics and the competition interface.
We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of exactly solvable models. Stationary cocycles are constructed for this pe
We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. In a previous paper we constructed stationary coc
In recent years, the application potential of visible light communication (VLC) technology as an alternative and supplement to radio frequency (RF) technology has attracted peoples attention. The study of the underlying VLC channel is the basis for d
We consider Gaussian approximation in a variant of the classical Johnson-Mehl birth-growth model with random growth speed. Seeds appear randomly in $mathbb{R}^d$ at random times and start growing instantaneously in all directions with a random speed.
The forecasting problem for a stationary and ergodic binary time series ${X_n}_{n=0}^{infty}$ is to estimate the probability that $X_{n+1}=1$ based on the observations $X_i$, $0le ile n$ without prior knowledge of the distribution of the process ${X_