Microsoft

Limits of dense graph sequences

We show that if a sequence of dense graphs has the property that for every fixed graph F, the density of copies of F in these graphs tends to a limit, then there is a natural “limit object”, namely a ...
JSTOR Daily

On the Convergence and Limits of Certain Matrix Sequences Arising in Quasi-Birth-and-Death Markov Chains

Journal of Applied Probability, Vol. 38, No. 2 (Jun., 2001), pp. 519-541 (23 pages) We study the convergence of certain matrix sequences that arise in quasi-birth-and-death (QBD) Markov chains and we ...
Microsoft

Limits of randomly grown graph sequences

Motivated in part by various sequences of graphs growing under random rules (like internet models), convergent sequences of dense graphs and their limits were introduced by Borgs, Chayes, Lovász, Sós ...
JSTOR Daily

Irrationality of Limits of Quickly Convergent Algebraic Numbers Sequences

Proceedings of the American Mathematical Society, Vol. 102, No. 3 (Mar., 1988), pp. 473-479 (7 pages) We present criteria for irrationality of limits of convergent sequences of rational numbers, ...