2011/05/26 by Uwe Schwerdtfeger, Schwerdtfeger, Uwe
Mathematics · #60C05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60C05
paper · pdf · doi:10.48550/arxiv.1105.5175
33 pages, 1 figure
arxiv created 2011/12/13 · arxiv updated 2011/12/14
We study limit distributions for random variables defined in terms of coefficients of a power series which is determined by a certain linear functional equation. Our technique combines the method of moments with the kernel method of algebraic combinatorics. As limiting distributions the area distributions of the Brownian excursion and meander occur. As combinatorial applications we compute the area laws for discrete excursions and meanders with an arbitrary finite set of steps and the area distribution of column convex polyominoes. As a by-product of our approach we find the joint distribution of area and final altitude for meanders with an arbitrary step set, and for unconstrained Bernoulli walks (and hence for Brownian Motion) the joint distribution of signed areas and final altitude. We give these distributions in terms of their moments.