Related papers: Sparse graph limits, entropy maximization and tran…
Subgraph densities have been defined, and served as basic tools, both in the case of graphons (limits of dense graph sequences) and graphings (limits of bounded-degree graph sequences). While limit objects have been described for the…
In this paper, we study convergence of coupled dynamical systems on convergent sequences of graphs to a continuum limit. We show that the solutions of the initial value problem for the dynamical system on a convergent graph sequence tend to…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…
For random combinatorial optimization problems, there has been much progress in establishing laws of large numbers and computing limiting constants for the optimal value of various problems. However, there has not been as much success in…
We consider self-loops and multiple edges in the configuration model as the size of the graph tends to infinity. The interest in these random variables is due to the fact that the configuration model, conditioned on being simple, is a…
Following a general program of studying limits of discrete structures, and motivated by the theory of limit objects of converge sequences of dense simple graphs, we study the limit of graph sequences such that every edge is labeled by an…
Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…
The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in…
Link prediction systems (e.g. recommender systems) typically use graph topology as one of their main sources of information. However, automorphisms and related properties of graphs beget inherent limits in predictability. We calculate hard…
In the dense graph limit theory, the topology of the set of graphs is defined by the distribution of the subgraphs spanned by finite number of random vertices. Vera T. S\'os proposed a question that if we consider only the number of edges…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
We study a non-exchangeable multi-agent system and rigorously derive a strong form of the mean-field limit. The convergence of the connection weights and the initial data implies convergence of large-scale dynamics toward a deterministic…
We couple projective limits of probability measures to direct limits of their symmetry groups. We show that the direct limit group is the group of symmetries of the projective limit probability measure. If projective systems of probability…
Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…
We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic…
We study an inhomogeneous sparse random graph on [N] = {1, . . . , N } as introduced in a seminal paper by Bollobas, Janson and Riordan (2007): vertices have a type (here in a compact metric space S), and edges between different vertices…
We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…
In this paper we consider a natural extremal graph theoretic problem of topological sort, concerning the minimization of the (topological) connectedness of the independence complex of graphs in terms of its dimension. We observe that the…
We generalize the notion of quasirandom which concerns a class of equivalent properties that random graphs satisfy. We show that the convergence of a graph sequence under the spectral distance is equivalent to the convergence using the…