554 citations · 1.7k across the 51 of their papers we have counts for
34 papers · 1 filter
Counting subgraphs in bounded-size Achlioptas processes
Mihyun Kang, Oliver Riordan
Achlioptas processes such as the Bohman--Frieze process are much harder to analyse than the classical Erdős--Rényi process, due to the dependence between edges added at different s…
Sesqui-type branching processes
Svante Janson, Oliver Riordan, Lutz Warnke
We consider branching processes consisting of particles (individuals) of two types (type L and type S) in which only particles of type L have offspring, proving estimates for the s…
The phase transition in bounded-size Achlioptas processes
Oliver Riordan, Lutz Warnke
Perhaps the best understood phase transition is that in the component structure of the uniform random graph process introduced by Erdős and Rényi around 1960. Since the model is so…
A local limit theorem for Quicksort key comparisons via multi-round smoothing
Béla Bollobás, James Allen Fill, Oliver Riordan
As proved by Régnier and Rösler, the number of key comparisons required by the randomized sorting algorithm QuickSort to sort a list of distinct items (keys) satisfies a global…
The threshold for jigsaw percolation on random graphs
Béla Bollobás, Oliver Riordan, Erik Slivken +1
Jigsaw percolation is a model for the process of solving puzzles within a social network, which was recently proposed by Brummitt, Chatterjee, Dey and Sivakoff. In the model there…
Exploring hypergraphs with martingales
Béla Bollobás, Oliver Riordan
Recently, we adapted exploration and martingale arguments of Nachmias and Peres, in turn based on ideas of Martin-Löf, Karp and Aldous, to prove asymptotic normality of the number…