Showing papers by "Michael Drmota published in 1997"
Book•
20 Mar 1997819 citations
TL;DR: In this article, the authors discuss the asymptotic properties of the coefficients of generating functions which satisfy a system of functional equations and show that under certain general conditions these coefficients are related to the distribution of a multivariate random variable.
Abstract: The aim of this paper is to discuss the asymptotic properties of the coefficients of generating functions which satisfy a system of functional equations. It turns out that under certain general conditions these coefficients are related to the distribution of a multivariate random variable that is asymptotically normal. As an application it turns out that the distribution of the terminal symbols in context-free languages is typically asymptotically normal. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 10, 103–124 (1997)
162 citations
TL;DR: In this paper, a plane rooted tree with n nodes is regarded as family tree of a Galton-Watson branching process conditioned on the total progeny, and it is shown that these two processes converge weakly to Brownian excursion local time.
Abstract: Let T be a plane rooted tree with n nodes which is regarded as family tree of a Galton-Watson branching process conditioned on the total progeny. The profile of the tree may be described by the number of nodes or the number of leaves in layer , respectively. It is shown that these two processes converge weakly to Brownian excursion local time. This is done via characteristic functions obtained by means of generating functions arising from the combinatorial setup and complex contour integration. Besides, an integral representation for the two-dimensional density of Brownian excursion local time is derived. © 1997 John Wiley & Sons, Inc. Random Struct. Alg.,10, 421–451, 1997
83 citations
TL;DR: A general theorem is presented that can be used to identify the limiting distribution for a class of combinatorial schemata and can derive the limiting distributions of those points with a given number of total predecessors.
Abstract: We present a general theorem that can be used to identify the limiting distribution for a class of combinatorial schemata. For example, many parameters in random mappings can be covered in this way. In particular, we can derive the limiting distribution of those points with a given number of total predecessors.
35 citations
01 Jan 1997
TL;DR: In this article, the authors considered a decomposable e branching process with two types of particles T 1, T 2 such that particles of type T 2 can only produce particles of types T 1 and T 2, whereas particles of Type T 1 can produce both types.
Abstract: Let us consider a decomposable e branching process with two types of particles T 1, T2 such that particles of type T 2 can only produce particles of types T 1 whereas particles of type T 1 can produce particles of both types. The aim of this paper is to characterize the kind of distribution of the particles of types T1 and T 2 when the total number n of all particles is fixed. Especially we are interested in the limit case n — ∞. It turns out that depending on the parameters of the process a number of different limiting distributions, e.g. normal or x 2 distributions, appear.
6 citations