76 citations · 533 across the 32 of their papers we have counts for
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Convergence of Achlioptas processes via differential equations with unique solutions
Oliver Riordan, Lutz Warnke
In Achlioptas processes, starting from an empty graph, in each step two potential edges are chosen uniformly at random, and using some rule one of them is selected and added to the…
Achlioptas processes are not always self-averaging
Oliver Riordan, Lutz Warnke
We consider a class of percolation models, called Achlioptas processes, discussed in [Science 323, 1453 (2009)] and [Science 333, 322 (2011)]. For these the evolution of the order…
Achlioptas process phase transitions are continuous
Oliver Riordan, Lutz Warnke
It is widely believed that certain simple modifications of the random graph process lead to discontinuous phase transitions. In particular, starting with the empty graph on ver…
The C_\ell-free process
Lutz Warnke
The C_\ell-free process starts with the empty graph on n vertices and adds edges chosen uniformly at random, one at a time, subject to the condition that no copy of C_\ell is creat…