2014/12/18 by Eric Cator, Cator, Eric, Henk Don +1
Mathematics · #60J80 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J80
paper · pdf · doi:10.48550/arxiv.1412.5890
16 pages, 2 figures
arxiv created 2014/12/18 · arxiv updated 2014/12/19
We investigate conditioning Galton-Watson trees on general recursive-type events, such as the event that the tree survives until a specific level. It turns out that the conditioned tree is again a type of Galton-Watson tree, with different types of offspring and a level-dependent offspring distribution, which will all be given explicitly. As an interesting application of these results, we will calculate the expected cost of searching a tree until reaching a given level.