arXiv research

The random graph is an infinite graph with the universal property that any embedding of $G-v$ extends to an embedding of $G$, for any finite graph. In this paper we show that this graph embeds in the curve graph of a surface $Σ$ if and only if $Σ$ has infinite genus, showing that the curve system on an infinite genus s…

Paper studies statistical tests on infinite random graphs.

Study geodesics on graphs with random lengths, proving bi-infinite paths exist.

The article studies random infinite ideal hyperbolic polyhedra and their dual graphs, establishing new boundary theories.

GCNs distinguish graph models based on embeddings, but depth matters.

Study the dynamics and topology of random hyperbolic manifolds.

We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Mark…

A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability …

GCNs struggle to distinguish certain graph models, especially those with high degree profiles.

We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers $\mathbb{N}$ via a Poisson point process with mean measure $Λ$ on the power set of $\mathbb{N}$. Each $E\in\cate$ has a least monotone cover in $\catf$, the collection of monotone subsets of $\cate$, an…

Graphs with bounded degrees and non-negative Ollivier-Ricci curvature have subexponential growth and diffusive random walk.

The paper shows subexponential growth and displacement bounds for random walks on graphs with bounded degrees and non-negative curvature.

Researchers explore statistical perspectives to understand GNN generalization.

First-passage percolation affects graph properties like curvature and geodesics.

Generative model connects random walk vertices to form networks, tractable for estimation and inference.

Study of lamplighter group's Cayley graph spectrum and random Schrödinger operators.

The paper proposes a Gaussian mixture model for Hilbert-space-valued data.

Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously shown by Belkin and Niyogi \cite{belkin_niyogi:2007} that the eigenvectors and eige…

Infinite diameter found in compression body graph.

DGP learns speech recognition by modeling complex relationships between utterances.

GGP models multivariate time series with latent sub-sequences for diverse behaviors.

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inf…

Data-driven methods link graphon limits to random walks and spectral clustering.

The study examines convergence of stochastic processes on large graphs and adjacency matrices.

Every infinitely edge-connected graph has a minor of Farey graph or $T_{\aleph_0}\ast t$.

The study connects geodesic flows on Riemann surfaces to random walks on their dual graphs.

The paper explores non-amenability in infinite-type surfaces and graphs.

We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the graphs we construct are generally connected, infinite diameter a…

Study flip graphs for surfaces of infinite type, finding uncountably many connected components.

Parabolic mapping class acts on curve graphs of infinite type surfaces.

Project infinite time series graphs to finite marginal models using number theory.

Study of harmonic functions on infinite penny graphs.

Study of mapping class groups on infinite graphs, focusing on their large-scale geometry.

Study polynomial growth harmonic functions on infinite penny graphs.

We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite diameter; this extends a recent result of J. Bavard to a large class of punctured sur…

Generates special homeomorphisms for complex surfaces.

Study of flip graphs and their automorphism groups for infinite-type surfaces.

Graph Lie algebras have infinite prolongation if they have a vertex of degree one.

Develops a universal test for assessing dynamic network models.

Study of infinite-type surfaces' automorphisms and graph structures.

Study reconstructs hidden perfect matchings in random graphs with specific edge weights.

Study of mapping class groups of infinite graphs, focusing on their finiteness and commensurability.

The paper extends graph complexity calculations for certain 3-manifolds up to 14.

Study shows surfaces without certain curves have infinite orbit graph.

New simplicial complex for infinite-type surfaces shows graph properties.

Graph of groups palindromic width mostly infinite.

Paper shows isomorphic curve graphs imply homeomorphic surfaces.

Two graphs on infinite-type surfaces have finite diameter and related automorphism groups.