## The Annals of Applied Probability

### Differential Equations for Random Processes and Random Graphs

Nicholas C. Wormald

#### Abstract

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.

#### Article information

Source
Ann. Appl. Probab., Volume 5, Number 4 (1995), 1217-1235.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aoap/1177004612

Digital Object Identifier
doi:10.1214/aoap/1177004612

Mathematical Reviews number (MathSciNet)
MR1384372

Zentralblatt MATH identifier
0847.05084

JSTOR