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First-passage percolation on width-two stretches with exponential link weights
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Eckhard Schlemm, Zentrum Mathematik, Technische Universität München
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Abstract
We consider the first-passage percolation problem on effectively one-dimensional graphs with vertex set {1,...,n}×{0,1} and translation-invariant edge-structure. For three of six non-trivial cases we obtain exact expressions for the asymptotic percolation rate χ by solving certain recursive distributional equations and invoking results from ergodic theory to identify χ as the expected asymptotic one-step growth of the first-passage time from (0,0) to (n,0).
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Full text: PDF
Pages: 424-434
Published on: October 6, 2009
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Bibliography
-
M. Abramowitz and I.A. Stegun.
Handbook of mathematical functions with formulas, graphs, and
mathematical tables.
Dover Books on Advanced Mathematics, New York: Dover,| c1965,
Corrected edition, edited by Abramowitz, Milton; Stegun, Irene A., 1965.
-
L. Breiman.
Probability.
Addison Wesley Series in Statistics, Reading, Mass.: Addison
Wesley, 1968, 1968.
-
R. Durrett.
Probability: theory and examples.
Wadsworth & Brooks/Cole, 1991.
-
A. Flaxman, D. Gamarnik, and G.B. Sorkin.
First-Passage Percolation on a Width-2 Strip and the Path Cost in a
VCG Auction.
LECTURE NOTES IN COMPUTER SCIENCE, 4286:99, 2006.
-
R.L. Graham, M. Grötschel, and L. Lovász.
Handbook of Combinatorics.
MIT Press, 1995.
-
R. Jentzsch.
Über Integralgleichungen mit positivem Kern.
J. Reine Angew. Math, 141:235-244, 1912.
-
H. Kesten.
Aspects of first passage percolation.
Lecture Notes in Math, 1180:125-264, 1986.
-
E. Schlemm.
First-passage percolation on width-two stretches.
Master's thesis, Freie Universität Berlin, June 2008.
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Electronic Communications in Probability. ISSN: 1083-589X |
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