uu.seUppsala University Publications

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Convergence to the Tracy-Widom distribution for longest paths in a directed random graphPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2013 (English)In: Latin American Journal of Probability and Mathematical Statistics, ISSN 1980-0436, E-ISSN 1980-0436, Vol. 10, no 2, 711-730 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2013. Vol. 10, no 2, 711-730 p.
##### Keyword [en]

Random graph, last passage percolation, strong approximation, Tracy- Widom distribution
##### National Category

Probability Theory and Statistics
##### Identifiers

URN: urn:nbn:se:uu:diva-304258OAI: oai:DiVA.org:uu-304258DiVA: diva2:1014917
#####

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2016-10-23
##### In thesis

We consider a directed graph on the 2-dimensional integer lattice, placing a directed edge from vertex (i_{1},i_{2}) to (j_{1},j_{2}), whenever i_{1} ≤ j_{1}, i_{2} ≤ j_{2}, with probability p, independently for each such pair of vertices. Let L_{n,m} denote the maximum length of all paths contained in an n×m rectangle. We show that there is a positive exponent a, such that, if m/n^{a}→1, as n→∞, then a properly centered/rescaled version of L_{n,m} converges weakly to the Tracy-Widom distribution. A generalization to graphs with non-constant probabilities is also discussed.

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