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On Universal Representation of Random Graphs

Authors:	Andrzej?Korzeniowski author-information" > author-information__contact u-icon-before" > mailto:korzeniowski@uta.edu" title=" korzeniowski@uta.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Department of Mathematics, University of Texas at Arlington, 76019 Arlington, TX, USA

Abstract:	It is shown that every probability measure on the interval [0, 1] gives rise to a unique infinite random graph g on vertices {v₁, v₂, . . .} and a sequence of random graphs gn on vertices{v₁, . . . , v_n} such that . In particular, for Bernoulli graphs withstable property Q, can be strengthened to: probability space (, F, P), set of infinite graphsG(Q) , F with property Q such that $P (G_n(Q) rightarrow G(Q)) = 1 quad mathrm{and}quad mathbf{P}(G-n(Q)) = P(G_n(Q))$ .AMS Subject Classification: 05C80, 05C62.

Keywords:	Bernoulli graphs infinite random graphs representations
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