238 citations · 1.5k across the 41 of their papers we have counts for
47 papers
Density of states of randomly sprinkled graphs
Antti Knowles, Steffen Polzer
Independently at every vertex of a large core graph , we draw a random graph and connect to a subset of its vertices. This model of a randomly sprinkled graph ca…
Bernoulli flow for Erdős-Rényi graphs
Joscha Henheik, Antti Knowles
We study the eigenvalues and eigenvectors of the adjacency matrix of the Erdős-Rényi graph in the regime . We establish optimal isotropic de…
Semilocalization for inhomogeneous random graphs
Thomas Buc-d'Alché, Antti Knowles
We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has b…
The Euclidean theory as a limit of an inhomogeneous Bose gas
Cristina Caraci, Antti Knowles, Alessio Ranallo +1
We prove that the grand canonical Gibbs state of an interacting two-dimensional quantum Bose gas confined by a trapping potential converges to the complex Euclidean field theory wi…
Localized phase for the Erdős-Rényi graph
Johannes Alt, Raphael Ducatez, Antti Knowles
We analyse the eigenvectors of the adjacency matrix of the Erdős-Rényi graph for . We show the existence of a localized phas…
The Euclidean theory as a limit of an interacting Bose gas
Jürg Fröhlich, Antti Knowles, Benjamin Schlein +1
We prove that the complex Euclidean field theory with local quartic self-interaction in two dimensions arises as a limit of an interacting Bose gas at positive temperature, when th…