76 citations · 533 across the 32 of their papers we have counts for
12 papers · 1 filter
Preferential attachment without vertex growth: emergence of the giant component
Svante Janson, Lutz Warnke
We study the following preferential attachment variant of the classical Erdos-Renyi random graph process. Starting with an empty graph on n vertices, new edges are added one-by-one…
Upper tail bounds for Stars
Matas Šileikis, Lutz Warnke
For r \ge 2, let X be the number of r-armed stars K_{1,r} in the binomial random graph G_{n,p}. We study the upper tail \Pr(X \ge (1+ε)\E X), and establish exponential bounds which…
A counterexample to the DeMarco-Kahn Upper Tail Conjecture
Matas Šileikis, Lutz Warnke
Given a fixed graph H, what is the (exponentially small) probability that the number X_H of copies of H in the binomial random graph G_{n,p} is at least twice its mean? Studied int…
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…
On the missing log in upper tail estimates
Lutz Warnke
In the late 1990s, Kim and Vu pioneered an inductive method for showing concentration of certain random variables X. Shortly afterwards, Janson and Ruci{ń}ski developed an alternat…
On the critical probability in percolation
Svante Janson, Lutz Warnke
For percolation on finite transitive graphs, Nachmias and Peres suggested a characterization of the critical probability based on the logarithmic derivative of the susceptibility.…
The lower tail: Poisson approximation revisited
Svante Janson, Lutz Warnke
The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variable…
The evolution of subcritical Achlioptas processes
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…
The Janson inequalities for general up-sets
Oliver Riordan, Lutz Warnke
Janson and Janson, Luczak and Rucinski proved several inequalities for the lower tail of the distribution of the number of events that hold, when all the events are up-sets (increa…
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 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…