11 papers
Renormalisation of Inhomogeneous Random Graphs
Luca Avena, Diego Garlaschelli, Rajat Subhra Hazra +1
We consider inhomogeneous random graphs in which vertices are assigned i.i.d.\ random weights, pairs of distinct vertices are connected by an edge independently with a probability…
Co-evolving vertex and edge dynamics in dense graphs
Siva Athreya, Frank den Hollander, Adrian Röllin
We consider a random graph in which vertices can have one of two possible colours. Each vertex switches its colour at a rate that is proportional to the number of vertices of the o…
Self-repellent branching random walk
Anton Bovier, Lisa Hartung, Frank den Hollander
We consider a system of particles performing a discrete-time binary branching random walk with independent standard normal increments subject to a penalty $\b$ for every pair of pa…
On the principal eigenvectors of random Markov matrices
Jacob Calvert, Frank den Hollander, Dana Randall
We analyze the invariant distributions of continuous-time and discrete-time random walks on randomly weighted complete digraphs. These distributions correspond to the principal lef…
Homogeneous nucleation for two-dimensional Kawasaki dynamics
Simone Baldassarri, Alexandre Gaudillière, Frank den Hollander +3
This is the third in a series of three papers in which we study a lattice gas subject to Kawasaki dynamics at inverse temperature in a large finite box $Î_β\subset \mathbb…
Tame sparse exponential random graphs
Suman Chakraborty, Remco van der Hofstad, Frank den Hollander
In this paper, we obtain a precise estimate of the probability that the sparse binomial random graph contains a large number of vertices in a triangle. The estimate of log of this…