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First-Passage Percolation with Exponential Times on a Ladder
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2010 (English)In: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 19, no 4, 593-601 p.Article in journal (Refereed) Published
Abstract [en]

We consider first-passage percolation on a ladder, i.e., the graph N x {0, 1}, where nodes at distance 1 are joined by an edge, and the times are exponentially i.i.d. with mean 1. We find an appropriate Markov chain to calculate an explicit expression for the time constant whose numerical value is approximate to 0.6827. This time constant is the long-term average inverse speed of the process. We also calculate the average residual time.

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2010. Vol. 19, no 4, 593-601 p.
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URN: urn:nbn:se:uu:diva-136164DOI: 10.1017/S0963548310000052ISI: 000279038700007OAI: oai:DiVA.org:uu-136164DiVA: diva2:376395
Available from: 2010-12-10 Created: 2010-12-10 Last updated: 2011-03-01Bibliographically approved

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