117 citations · 561 across the 64 of their papers we have counts for
72 papers
Network evolution with self-reinforcement
Shankar Bhamidi, Remco van der Hofstad, Frank den Hollander +1
We study a new class of preferential attachment trees with \emph{self-reinforcement}. At each time, each vertex is assigned a weight equal to the cumulative sum over past times of…
The Triangle Friendship Paradox
Bishakh Bhattacharya, Nitya Gadhiwala, Frank den Hollander +2
We consider the generalised friendship paradox, focussing on the number of triangles at a vertex as the relevant attribute. We show that, contrary to the setting where the attribut…
The friendship paradox for trees
Rajat Subhra Hazra, Frank den Hollander, Nelly Litvak +1
We analyse the friendship paradox on finite and infinite trees. In particular, we monitor the vertices for which the friendship-bias is positive, neutral and negative, respectively…
The multi-level friendship paradox for sparse random graphs
Rajat Subhra Hazra, Frank den Hollander, Azadeh Parvaneh
In Hazra, den Hollander and Parvaneh (2025) we analysed the friendship paradox for sparse random graphs. For four classes of random graphs we characterised the empirical distributi…
Evolution of Discordance
F. den Hollander
The present paper is a brief overview of random opinion dynamics on random graphs based on the Ising Lecture given by the author at the World Congress in Probability and Statistics…
Interacting Particle Systems on Random Graphs
F. Capannoli, F. den Hollander
The present overview of interacting particle systems on random graphs collects the notes of a mini-course given by the authors at the Brazilian School of Probability, 5--9 August 2…
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…
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…
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 $Λ_β\subset \mathbb{Z}…
The Moran model with random resampling rates
Siva Athreya, Frank den Hollander, Adrian Röllin
In this paper we consider the two-type Moran model with individuals. Each individual is assigned a resampling rate, drawn independently from a probability distribution ${\mathb…
Largest Eigenvalue of the Configuration Model and Breaking of Ensemble Equivalence
Pierfrancesco Dionigi, Diego Garlaschelli, Rajat Subhra Hazra +1
We analyse the largest eigenvalue of the adjacency matrix of the configuration model with large degrees, where the latter are treated as hard constraints. In particular, we compute…
The friendship paradox for sparse random graphs
Rajat Subhra Hazra, Frank den Hollander, Azadeh Parvaneh
Let be an undirected finite graph on vertices labelled by . For , let be the friendship bias of vertex , define…
Continuum graph dynamics via population dynamics: well-posedness, duality and equilibria
Andreas Greven, Frank den Hollander, Anton Klimovsky +1
This paper introduces graphemes for constructing and analyzing stochastic processes that describe the evolution of large dynamic graphs. Unlike graphons, which capture the static p…
Quenched large deviations in renewal theory
Frank den Hollander, Marco Zamparo
In this paper we introduce and study renewal-reward processes in random environments where each renewal involves a reward taking values in a Banach space. We derive quenched large…
The annealed parabolic Anderson model on a regular tree
Frank den Hollander, Daoyi Wang
We study the total mass of the solution to the parabolic Anderson model on a regular tree with an i.i.d. random potential whose marginal distribution is double-exponential. In earl…
Large deviation principle for the norm of the Laplacian matrix of inhomogeneous Erdős-Rényi random graphs
Rajat Subhra Hazra, Frank den Hollander, Maarten Markering
We consider an inhomogeneous Erdős-Rényi random graph with vertex set for which the pair of vertices , , is connected by an edge w…
Droplet dynamics in a two-dimensional rarefied gas under Kawasaki dynamics
Simone Baldassarri, Alexandre Gaudillière, Frank den Hollander +3
This is the second in a series of three papers in which we study a lattice gas subject to Kawasaki conservative dynamics at inverse temperature in a large finite box $Λ_β\sub…
Graphon-valued processes with vertex-level fluctuations
Peter Braunsteins, Frank den Hollander, Michel Mandjes
We consider a class of graph-valued stochastic processes in which each vertex has a type that fluctuates randomly over time. Collectively, the paths of the vertex types up to a giv…
Sparse random graphs with many triangles
Suman Chakraborty, Remco van der Hofstad, Frank den Hollander
In this paper we consider the Erdős-Rényi random graph in the sparse regime in the limit as the number of vertices tends to infinity. We are interested in what this graph looks…
Spatially Inhomogeneous Populations with Seed-banks: II. Clustering Regime
Frank den Hollander, Shubhamoy Nandan
We consider a spatial version of the classical Moran model with seed-banks where the constituent populations have finite sizes. Individuals live in colonies labelled by $\mathbb{Z}…
Switching interacting particle systems: scaling limits, uphill diffusion and boundary layer
Simone Floreani, Cristian Giardinà, Frank den Hollander +2
In this paper we consider three classes of interacting particle systems on : independent random walks, the exclusion process, and the inclusion process. We allow particl…
Metastability for Glauber dynamics on the complete graph with coupling disorder
Anton Bovier, Frank den Hollander, Saeda Marello
Consider the complete graph on vertices. To each vertex assign an Ising spin that can take the values or . Each spin interacts with a magn…
Breaking of ensemble equivalence for dense random graphs under a single constraint
Frank den Hollander, Maarten Markering
Two ensembles are often used to model random graphs subject to constraints: the microcanonical ensemble (= hard constraint) and the canonical ensemble (= soft constraint). It is sa…
The Parabolic Anderson Model on a Galton-Watson tree revisited
Frank den Hollander, Daoyi Wang
In [1] a detailed analysis was given of the large-time asymptotics of the total mass of the solution to the parabolic Anderson model on a supercritical Galton-Watson random tree wi…