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Achlioptas processes and truncated stochastic coalescence

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  • UserLutz Warnke (University of Cambridge)
  • ClockThursday 18 February 2016, 14:30-15:30
  • HouseMR12.

If you have a question about this talk, please contact Andrew Thomason.

Achlioptas processes are widely-studied variants of the classical Erdős-Rényi random graph process. Starting from an empty graph, these proceed as follows: in each step two potential edges are chosen uniformly at random, and using some rule one of them is selected and added to the evolving graph. Very detailed results are nowadays known for the class of `bounded-size’ rules, where all component sizes larger than some constant B are treated the same way.

In 2001 Spencer and Wormald made several conjectures, which intuitively state that any `unbounded’ size rule (such as the sum or product rule) is in some sense the limit of a sequence of appropriately defined `truncated’ bounded-size rules (with increasing size-bound B). In this talk we shall discuss some of our recent work, which proves one of these conjectures.

This talk is part of the Combinatorics Seminar series.

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