Author
Tamás F. Móri
Other affiliations: Bowling Green State University, Alfréd Rényi Institute of Mathematics
Bio: Tamás F. Móri is an academic researcher from Eötvös Loránd University. The author has contributed to research in topics: Random graph & Population. The author has an hindex of 16, co-authored 93 publications receiving 1188 citations. Previous affiliations of Tamás F. Móri include Bowling Green State University & Alfréd Rényi Institute of Mathematics.
Papers published on a yearly basis
Papers
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TL;DR: In a one-parameter model for evolution of random trees, strong law of large numbers and central limit theorem are proved for the number of vertices with low degree as discussed by the authors.
Abstract: In a one-parameter model for evolution of random trees strong law of large numbers and central limit theorem are proved for the number of vertices with low degree. The proof is based on elementary martingale theory.
349 citations
TL;DR: The law of large numbers and the central limit theorem are proved for the maximal degree in a one-parameter model for evolution of random trees.
Abstract: In a one-parameter model for evolution of random trees, which also includes the Barabasi–Albert random graph [1], the law of large numbers and the central limit theorem are proved for the maximal degree. In the proofs martingale methods are applied.
141 citations
TL;DR: In this paper, it was shown that for any fixed Pearson correlation coefficient strictly between − 1 and 1, the distance correlation coefficient can take any value in the open unit interval ( 0, 1 ).
130 citations
TL;DR: In this paper, a multivariate analogue of skewness and kurtosis was proposed for infinitely divisible distributions, and it was shown that k + 2d can be computed for infinitely distributed distributions.
Abstract: Let X be a d-dimensional standardized random variable $({\bf E}(X) = 0, \operatorname{cov} (X) = 1)$. Then for a multivariate analogue of skewness $s = {\bf E}(\| X \|^2 X)$ and kurtosis $k = {\bf E}XX^T XX^T - (d + 2)I$ we show that $\| s \|^2 \leqq {\text{tr}}\, k + 2d$. For infinitely divisible distributions $\| s \|^2 \leqq {\text{tr }}k$.
91 citations
TL;DR: In this paper, the same method was applied for proving Bonferroni-Galambos-type inequalities, and the lower and upper bounds of S m were given in terms of S k and S l.
Abstract: Let A 1 , A 2 , · ··, A n be events on a probability space. Denote by S k the k th binomial moment of the number M n of those A 's which occur. Sharp lower and upper bounds of S m will be given in terms of S k and S l . The same method can be applied for proving Bonferroni–Galambos-type inequalities.
40 citations
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TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.
5,689 citations
01 Jan 1977
TL;DR: In the Hamadryas baboon, males are substantially larger than females, and a troop of baboons is subdivided into a number of ‘one-male groups’, consisting of one adult male and one or more females with their young.
Abstract: In the Hamadryas baboon, males are substantially larger than females. A troop of baboons is subdivided into a number of ‘one-male groups’, consisting of one adult male and one or more females with their young. The male prevents any of ‘his’ females from moving too far from him. Kummer (1971) performed the following experiment. Two males, A and B, previously unknown to each other, were placed in a large enclosure. Male A was free to move about the enclosure, but male B was shut in a small cage, from which he could observe A but not interfere. A female, unknown to both males, was then placed in the enclosure. Within 20 minutes male A had persuaded the female to accept his ownership. Male B was then released into the open enclosure. Instead of challenging male A , B avoided any contact, accepting A’s ownership.
2,364 citations
Book•
01 Jan 2007TL;DR: The Erdos-Renyi random graphs model, a version of the CHKNS model, helps clarify the role of randomness in the distribution of values in the discrete-time world.
Abstract: 1. Overview 2. Erdos-Renyi random graphs 3. Fixed degree distributions 4. Power laws 5. Small worlds 6. Random walks 7. CHKNS model.
1,010 citations
01 Jan 2017
TL;DR: This chapter explains why many real-world networks are small worlds and have large fluctuations in their degrees, and why Probability theory offers a highly effective way to deal with the complexity of networks, and leads us to consider random graphs.
Abstract: This rigorous introduction to network science presents random graphs as models for real-world networks. Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. Designed for a master's-level course, where students may only have a basic background in probability, the text covers such important preliminaries as convergence of random variables, probabilistic bounds, coupling, martingales, and branching processes. Building on this base - and motivated by many examples of real-world networks, including the Internet, collaboration networks, and the World Wide Web - it focuses on several important models for complex networks and investigates key properties, such as the connectivity of nodes. Numerous exercises allow students to develop intuition and experience in working with the models.
934 citations
Book•
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01 Jan 1982
TL;DR: Theorem of Borsuk and Topological Transversality as mentioned in this paper, the Lefschetz-Hopf Theory, and fixed point index are the fundamental fixed point theorem.
Abstract: Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index
688 citations