Related papers: Stochastic incompleteness for graphs and weak Omor…
We generalize the weak Omori-Yau maximum principle to the setting of strongly local Dirichlet forms. As an application, we obtain an analytic approach to compare the stochastic completeness of a weighted graph with that of an associated…
The goal of this article is to survey various results concerning stochastic completeness of graphs. In particular, we present a variety of formulations of stochastic completeness and discuss how a discrepancy between uniqueness class and…
This note shows how Condition 1 in Okumura (2025) can be tested efficiently using a standard graph-theoretic algorithm. It also describes an efficient implementation of Okumura's mechanism.
We study non-linear Schr\"odinger operators on graphs. We construct minimal nonnegative solutions to corresponding semi-linear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a non-linear…
The aim of this paper is to introduce new forms of the weak and Omori-Yau maximum principles for linear operators, notably for trace type operators, and show their usefulness, for instance, in the context of PDE's and in the theory of…
We survey geometric properties which imply the stochastic incompleteness of the minimal diffusion process associated to the Laplacian on manifolds and graphs. In particular, we completely characterize stochastic incompleteness for…
Using a deep criteria due to Pigola, Rigoli and Setti, we prove that a geodesically complete, properly immersed submanifold M of a stochastically complete Riemannian manifold N is stochastically complete. This implies that the weak…
In this paper, we establish a generalized maximum principle for pseudo-Hermitian manifolds. As corollaries, Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced. Moreover, we prove that the stochastic completeness…
In this thesis, we analyze the stochastic completeness of a heat kernel on graphs which is a function of three variables: a pair of vertices and a continuous time, for infinite, locally finite, connected graphs. For general graphs, a…
We study the connections between volume growth, spectral properties and stochastic completeness of locally finite graphs. For a class of graphs with a very weak spherical symmetry we give a condition which implies both stochastic…
Most of the existing works on provable guarantees for low-rank matrix completion algorithms rely on some unrealistic assumptions such that matrix entries are sampled randomly or the sampling pattern has a specific structure. In this work,…
We establish thresholds for the feasibility of random multi-graph alignment in two models. In the Gaussian model, we demonstrate an "all-or-nothing" phenomenon: above a critical threshold, exact alignment is achievable with high…
We construct optimal Hardy weights to subcritical energy functionals $h$ associated with quasilinear Schr\"odinger operators on locally finite graphs. Here, optimality means that the weight $w$ is the largest possible with respect to a…
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…
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 prove an asymptotic multipartite version of a well-known theorem of K\"uhn and Osthus by establishing, for any graph $H$ with chromatic number $r$, the asymptotic multipartite minimum degree threshold which ensures that a…
In recent years, researchers proposed several algorithms that compute metric quantities of real-world complex networks, and that are very efficient in practice, although there is no worst-case guarantee. In this work, we propose an…
As introduced by Bollob\'as, a graph $G$ is weakly $H$-saturated if the complete graph $K_n$ is obtained by iteratively completing copies of $H$ minus an edge. For all graphs $H$, we obtain an asymptotic lower bound for the critical…
A graph is strongly perfect if every induced subgraph H has a stable set that meets every nonempty maximal clique of H. The characterization of strongly perfect graphs by a set of forbidden induced subgraphs is not known. Here we provide…
The one-inclusion graph algorithm of Haussler, Littlestone, and Warmuth achieves an optimal in-expectation risk bound in the standard PAC classification setup. In one of the first COLT open problems, Warmuth conjectured that this prediction…