论文信息 - Last Passage Percolation in Macroscopically Inhomogeneous Media

Last Passage Percolation in Macroscopically Inhomogeneous Media

In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a variational problem that provides an ODE for the deterministic limiting shape of the maximal path. We obtain a sufficient analytical condition for uniquenes of the solution for the variational problem. Consequences for the totally asymmetric simple exclusion process are discussed.

Leonardo T. Rolla | A. Teixeira | Augusto Q. Teixeira | L. Rolla

[1] Current Fluctuations for the Totally Asymmetric Simple Exclusion Process , 2001, cond-mat/0101200.

[2] T. Seppäläinen. Hydrodynamic Profiles for the Totally Asymmetric Exclusion Process with a Slow Bond , 2000 .

[3] THE MOTION OF A SECOND CLASS PARTICLE FOR THE TASEP STARTING FROM A DECREASING SHOCK PROFILE , 2005, math/0505216.

[4] Ben Hambly,et al. Heavy tails in last-passage percolation , 2006, math/0604189.

[6] Jinho Baik,et al. Optimal tail estimates for directed last passage site percolation with geometric random variables , 2001 .

[7] On convergence of moments for random Young tableaux and a random growth model , 2001, math/0108008.

[9] Neil O'Connell,et al. Random matrices, non-colliding processes and queues , 2002, math/0203176.

[10] A GUE central limit theorem and universality of directed first andlast passage site percolation , 2004, math/0412369.

[11] P. Glynn,et al. Departures from Many Queues in Series , 1991 .

[12] Competition interfaces and second class particles , 2004, math/0406333.

[13] J. Krug,et al. Hydrodynamics and Platoon Formation for a Totally Asymmetric Exclusion Model with Particlewise Disorder , 1999 .

[14] Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process , 2006 .

[15] K. Johansson. Shape Fluctuations and Random Matrices , 1999, math/9903134.