Related papers: Asymptotic Distribution of Parameters in Random Ma…
We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…
We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…
We find new upper bounds on the size of a minimum totally dominating set for random regular graphs and for regular graphs with large girth. These bounds are obtained through the analysis of a local algorithm using a method due to Hoppen and…
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
We find precise asymptotic estimates for the number of planar maps and graphs with a condition on the minimum degree, and properties of random graphs from these classes. In particular we show that the size of the largest tree attached to…
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy tailed distributions of the structure width. When…
We study the evolution of a random graph under the constraint that the diameter remain constant as the graph grows. We show that if the graph maintains the form of its link distribution it must be scale-free with exponent between 2 and 3.…
Given connected graph $H$ which is not a star, we show that the number of copies of $H$ in a dense uniformly random regular graph is asymptotically Gaussian, which was not known even for $H$ being a triangle. This addresses a question of…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
We study the asymptotic behaviour of the maximum interpoint distance of random points in a planar bounded set with an unique major axis and a boundary behaving like an ellipse at the endpoints. Our main result covers the case of uniformly…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
We present the theory of linear rank-metric codes from the point of view of their fundamental parameters. These are: the minimum rank distance, the rank distribution, the maximum rank, the covering radius, and the field size. The focus of…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
Recently, Bollob\'as, Janson and Riordan introduced a very general family of random graph models, producing inhomogeneous random graphs with $\Theta(n)$ edges. Roughly speaking, there is one model for each {\em kernel}, i.e., each symmetric…
We establish the asymptotic distribution of likelihood ratio tests (LRTs) in settings where some of the nuisance parameters are unidentifiable under the null hypothesis, parameters of interest lie on the boundary of the parameter space, and…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Although its probability mass function (pmf) is known, what is lacking is a $visual$…
We study the asymptotic distributions of the number of crossings and the number of simple chords in a random chord diagram. Using size-bias coupling and Stein's method, we obtain bounds on the Kolmogorov distance between the distribution of…
In this thesis the properties of two kinds of non-uniform random recursive trees are studied. In the first model weights are assigned to each node, thus altering the attachment probabilities. We will call these trees weighted recursive…