Abstract
We study a variant of poly-nuclear growth where the level boundaries perform continuous-time, discrete-space random walks, and study how its asymptotic behavior is affected by the presence of a columnar defect on the line. We prove that there is a non-trivial phase transition in the strength of the perturbation, above which the law of large numbers for the height function is modified.
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Aldous D., Diaconis P.: Hammersley’s interacting particle process and longest increasing subsequences. Probab. Theory Relat. Fields 103(2), 199–213 (1995)
Arias-Castro, E., Candes, E., Helgason, H., Zeitouni, O.: Searching for a trail of evidence in a maze. Preprint (2007) arXiv:math.ST/0701668v1
Arratia R.: The motion of a tagged particle in the simple symmetric exclusion process on Z. Ann. Probab. 11(2), 362–373 (1983)
Baik J., Deift P., Johansson K.: On the distribution of the length of the longest increasing subsequence of random permutations. J. Am. Math. Soc. 12(4), 1119–1178 (1999)
Baik, J., Rains, E.M.: Symmetrized random permutations. In: Random matrix models and their applications, Math. Sci. Res. Inst. Publ., vol. 40, pp. 1–19. Cambridge University Press, Cambridge (2001)
Beffara, V., Sidoravicius, V.: in preparation (2008)
Beffara, V., Sidoravicius, V., Spohn, H., Vares, M.: Polymer pinning in random medium as influence percolation. In: Den Hollander, F., Verbitsky, E. (eds.) Dynamics and Stochastics, IMS Lecture Notes Monograph Ser., vol. 48, pp. 1–15. Inst. Math. Statist (2006)
Chayes L., Schonmann R., Swindle G.: Lifshitz law for the volume of a two dimensional droplet at zero temperature. J. Stat. Phys. 79(4), 821–831 (1995)
Janowsky S.A., Lebowitz J.L.: Exact results for the asymmetric simple exclusion process with a blockage. J. Stat. Phys. 77(1–2), 35–51 (1994)
Kesten, H.: First-passage percolation. In: From classical to modern probability. Progr. Probab., vol. 54, pp. 93–143. Birkhäuser, Basel (2003)
Liggett T.M.: Interacting particle systems, Grundlehren der Mathematischen Wissenschaften, vol. 276. Springer, New York (1985)
Myllys, M., Maunuksela, J., Merikoski, J., Timonen, J., Horvath, V.K., Ha, M., den Nijs, M.: Effect of columnar defect on the shape of slow-combustion fronts. Preprint (2003). Cond-Mat/0307231
Prähofer, M., Spohn, H.: Scale invariance of the PNG droplet and the Airy process. J. Statist. Phys. 108(5–6), 1071–1106 (2002). Dedicated to David Ruelle and Yasha Sinai on the occasion of their 65th birthdays
Spohn H.: Interface motion in models with stochastic dynamics. J. Stat. Phys. 71(5–6), 1081–1132 (1993)
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Beffara, V., Sidoravicius, V. & Vares, M.E. Randomized polynuclear growth with a columnar defect. Probab. Theory Relat. Fields 147, 565–581 (2010). https://doi.org/10.1007/s00440-009-0216-8
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DOI: https://doi.org/10.1007/s00440-009-0216-8