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Competition interfaces and second class particles | Pablo A. Ferrari
; Leandro P. R. Pimentel
; | Date: |
16 Jun 2004 | Journal: | Annals of Probability 2005, Vol. 33, No. 4, 1235-1254 DOI: 10.1214/009117905000000080 | Subject: | Probability; Mathematical Physics MSC-class: 60K35 (Primary) 82B. (Secondary) | math.PR math-ph math.MP | Abstract: | The one-dimensional nearest-neighbor totally asymmetric simple exclusion process can be constructed in the same space as a last-passage percolation model in Z^2. We show that the trajectory of a second class particle in the exclusion process can be linearly mapped into the competition interface between two growing clusters in the last-passage percolation model. Using technology built up for geodesics in percolation, we show that the competition interface converges almost surely to an asymptotic random direction. As a consequence we get a new proof for the strong law of large numbers for the second class particle in the rarefaction fan and describe the distribution of the asymptotic angle of the competition interface. | Source: | arXiv, math.PR/0406333 | Services: | Forum | Review | PDF | Favorites |
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