We introduce and develop a theory of limits for sequences of sparse graphs based on $ L^ p
$ graphons, which generalizes both the existing $ L^\infty $ theory of dense graph limits and …

For any fixed simple graph H=(V, E) and any fixed u> 0, we establish the leading order of the
exponential rate function for the probability that the number of copies of H in the Erdős …

We present a new approach to graph limit theory that unifies and generalizes the two most
well-developed directions, namely dense graph limits (even the more general limits) and …

We present a new approach, based on graphon theory, to finding the limiting spectral
distributions of general Wigner‐type matrices. This approach determines the moments of the …

We extend the theory of probability graphons, continuum representations of edge-decorated
graphs arising in graph limits theory, to the'right convergence'point of view. First of all, we …

We study a metric on the set of finite graphs in which two graphs are considered to be similar
if they have similar bounded dimensional “factors”. We show that limits of convergent graph …

We set up a new notion of local convergence for permutations and we prove a
characterization in terms of proportions of consecutive pattern occurrences. We also …

How can we approximate sparse graphs and sequences of sparse graphs (with unbounded
average degree)? We consider convergence in the first k moments of the graph spectrum …

We develop further the graph limit theory for dense weighted graph sequences. In particular,
we consider probability graphons, which have recently appeared in graph limit theory as …

How can we approximate sparse graphs and sequences of sparse graphs (with unbounded
average degree)? We consider convergence in the first $ k $ moments of the graph …