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November, 1995 Differential Equations for Random Processes and Random Graphs
Nicholas C. Wormald
Ann. Appl. Probab. 5(4): 1217-1235 (November, 1995). DOI: 10.1214/aoap/1177004612


General criteria are given to ensure that in a family of discrete random processes, given parameters exhibit convergence to the solution of a system of differential equations. As one application we consider random graph processes in which the maximum degree is bounded and show that the numbers of vertices of given degree exhibit this convergence as the total number of vertices tends to infinity. Two other applications are to random processes which generate independent sets of vertices in random $r$-regular graphs. In these cases, we deduce almost sure lower bounds on the size of independent sets of vertices in random $r$-regular graphs.


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Nicholas C. Wormald. "Differential Equations for Random Processes and Random Graphs." Ann. Appl. Probab. 5 (4) 1217 - 1235, November, 1995.


Published: November, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0847.05084
MathSciNet: MR1384372
Digital Object Identifier: 10.1214/aoap/1177004612

Primary: 05C80

Keywords: $d$-process , Differential equations , Independent set , random graph , random process , random regular graph

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 4 • November, 1995
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