Riemann-Hilbert problems for last passage percolation

Abstract

Last three years have seen new developments in the theory of last passage percolation, which has variety applications to random permutations, random growth and random vicious walks. It turns out that a few class of models have determinant formulas for the probability distribution, which can be analyzed asymptotically. One of the tools for the asymptotic analysis has been the Riemann-Hilbert method. In this paper, we survey the use of Riemann-Hilbert method in the last passage percolation problems.

24 pages, 3 figures, AMS-LaTex

References in corpus (4)

• Level-Spacing Distributions and the Airy Kernel
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Statistical Self-Similarity of One-Dimensional Growth Processes
• Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlevé II Equation

Cited by in corpus (5)

• Exact scaling functions for one-dimensional stationary KPZ growth
• Distribution of the first particle in discrete orthogonal polynomial ensembles
• Discrete Painlevé equations and random matrix averages
• Growth models, random matrices and Painleve transcendents
• Discrete gap probabilities and discrete Painleve equations