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Keyword: stochastic processes ×Clear all

3 claims from 1 paper

1. Mathematics › Limits and Structures in Graph Theory

   Differential Equations for Random Processes and Random Graphs

   Wormald · The Annals of Applied Probability · 1995

   The paper gives general criteria for discrete random processes to follow differential equations, then applies them to bounded-degree random graph processes and to independent sets in random regular graphs.

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   1. UncheckedThe paper gives general criteria under which chosen parameters of a family of discrete random processes converge to the solution of a system of differential equations.“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.”
   2. Unchecked“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.”
   3. UncheckedUsing differential equations to analyse random processes, the paper derives almost sure lower bounds on independent set size 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.”