5 papers · 1 filter
Critical percolation on preferential attachment graphs with infinite variance
Peter Mörters, Lucas Schätze
We study the inhomogeneous random graph with preferential attachment kernel and degree distribution with power-law exponent as a representative of the class of graphs…
The critical percolation window in growing random graphs
Joost Jorritsma, Pascal Maillard, Peter Mörters
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to…
Crossing probabilities in geometric inhomogeneous random graphs
Emmanuel Jacob, Céline Kerriou, Amitai Linker +1
In a geometric inhomogeneous random graph vertices are given by the points of a Poisson process and are equipped with independent weights following a heavy tailed distribution. Any…
The fewest-big-jumps principle and an application to random graphs
Céline Kerriou, Peter Mörters
We prove a large deviation principle for the sum of n independent heavy-tailed random variables, which are subject to a moving cut-off boundary at location n. Conditional on the su…
Robustness in the Poisson Boolean model with convex grains
Peter Gracar, Marilyn Korfhage, Peter Mörters
We study the Poisson Boolean model where the grains are random convex bodies with a rotation-invariant distribution. We say that a grain distribution is dense if the union of the g…