175 research outputs found
Accuracy of approximation for discrete distributions
The paper is a contribution to the problem of estimating the deviation of two discrete probability distributions in terms of the supremum distance between their generating functions over the interval [ 0,1 ]. Deviation can be measured by the difference of the k th terms or by total variation distance. Our new bounds have better order of magnitude than those proved previously, and they are even sharp in certain cases. © 2016 Tamás F. Móri
Further properties of a random graph with duplications and deletions
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 analyze the limit distribution of the degree of a fixed vertex and derive a.s. asymptotic bounds for the maximal degree. The model shows a phase transition phenomenon with respect to the probabilities of duplication and deletion. © 2016 Taylor & Franci
Further properties of a random graph with duplications and deletions
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 analyze the limit distribution of the degree of a fixed vertex and derive a.s. asymptotic bounds for the maximal degree. The model shows a phase transition phenomenon with respect to the probabilities of duplication and deletion. © 2016 Taylor & Franci
ASYMPTOTIC PROPERTIES OF A RANDOM GRAPH WITH DUPLICATIONS
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an almost surely asymptotic degree distribution, with stretched exponential decay; more precisely, the proportion of vertices of degree d tends to some positive number c(d) > 0 almost surely as the number of steps goes to infinity, and c(d) similar to (e pi)(1/2)d(1/4)e(-2)root d holds as d -> infinity
Testing goodness-of-fit of random graph models
Random graphs are matrices with independent 0, 1 elements with probabilities
determined by a small number of parameters. One of the oldest model is the
Rasch model where the odds are ratios of positive numbers scaling the rows and
columns. Later Persi Diaconis with his coworkers rediscovered the model for
symmetric matrices and called the model beta. Here we give goodnes-of-fit tests
for the model and extend the model to a version of the block model introduced
by Holland, Laskey, and Leinhard
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