Asymptotic normality of the k-core in random graphs
نویسندگان
چکیده
منابع مشابه
ASYMPTOTIC NORMALITY OF THE k-CORE IN RANDOM GRAPHS
We study the k-core of a random (multi)graph on n vertices with a given degree sequence. In our previous paper [18] we used properties of empirical distributions of independent random variables to give a simple proof of the fact that the size of the giant k-core obeys a law of large numbers as n → ∞. Here we develop the method further and show that the fluctuations around the deterministic limi...
متن کاملAsymptotic Normality of the K - Core in Random Graphs 3
We study the k-core of a random (multi)graph on n vertices with a given degree sequence. In our previous paper [Random Structures Algorithms 30 (2007) 50–62] we used properties of empirical distributions of independent random variables to give a simple proof of the fact that the size of the giant k-core obeys a law of large numbers as n →∞. Here we develop the method further and show that the f...
متن کاملASYMPTOTIC NORMALITY OF THE k-CORE IN RANDOM GRAPHS BY SVANTE JANSON
We study the k-core of a random (multi)graph on n vertices with a given degree sequence. In our previous paper [Random Structures Algorithms 30 (2007) 50–62] we used properties of empirical distributions of independent random variables to give a simple proof of the fact that the size of the giant k-core obeys a law of large numbers as n→∞. Here we develop the method further and show that the fl...
متن کاملCDAM research report LSE-CDAM-2007-40 ASYMPTOTIC NORMALITY OF THE k-CORE IN RANDOM GRAPHS
We study the k-core of a random (multi)graph on n vertices with a given degree sequence. In our previous paper [18] we used properties of empirical distributions of independent random variables to give a simple proof of the fact that the size of the giant k-core obeys a law of large numbers as n→∞. Here we develop the method further and show that the fluctuations around the deterministic limit ...
متن کاملMonotonicity, asymptotic normality and vertex degrees in random graphs
We exploit a result by Nerman [23] which shows that conditional limit theorems hold when a certain monotonicity condition is satisfied. Our main result is an application to vertex degrees in random graphs where we obtain asymptotic normality for the number of vertices with a given degree in the random graph G(n, m) with a fixed number of edges from the corresponding result for the random graph ...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2008
ISSN: 1050-5164
DOI: 10.1214/07-aap478