59 citations · 95 across the 13 of their papers we have counts for
20 papers
On the accretivity and m-accretivity of Laplacians and porous medium-type operators on graphs
Davide Bianchi, Matthias Keller, Alberto G. Setti +1
We study the accretivity and m-accretivity of Laplacian and porous medium-type operators on weighted graphs. In particular, we give several conditions that imply these properties f…
Nonlinear parabolic characterizations of stochastic completeness at infinity on weighted graphs
Davide Bianchi, Bobo Hua, Alberto G. Setti +1
We prove a nonlinear parabolic characterization of stochastic completeness at infinity for weighted graphs. For the filtration equation \[ (\partial_t + ΔΦ)u =0 \] where is the…
The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation
Davide Bianchi, Bobo Hua, Alberto G. Setti +1
We study the Cauchy problem for the generalized porous medium equation on infinite weighted graphs. For a general nonlinearity, we establish Dirichlet comparison and weak maximum p…
The generalized porous medium equation on graphs: existence and uniqueness of solutions with data
Davide Bianchi, Alberto G. Setti, Radoslaw K. Wojciechowski
We study solutions of the generalized porous medium equation on infinite graphs. For nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild solut…
Essential self-adjointness and the -Liouville property
Bobo Hua, Jun Masamune, Radosław K. Wojciechowski
We discuss connections between the essential self-adjointness of a symmetric operator and the constancy of functions which are in the kernel of the adjoint of the operator. We then…
Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature
Radosław K. Wojciechowski
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 a…
Coverings and the heat equation on graphs: stochastic incompleteness, the Feller property and uniform transience
Bobo Hua, Florentin Münch, Radosław K. Wojciechowski
We study regular coverings of graphs and manifolds with a focus on properties of the heat equation. In particular, we look at stochastic incompleteness, the Feller property and uni…
Ollivier Ricci curvature for general graph Laplacians: Heat equation, Laplacian comparison, non-explosion and diameter bounds
Florentin Münch, Radoslaw K. Wojciechowski
Discrete time random walks on a finite set naturally translate via a one-to-one correspondence to discrete Laplace operators. Typically, Ollivier curvature has been investigated vi…
Note on uniformly transient graphs
Matthias Keller, Daniel Lenz, Marcel Schmidt +1
We study a special class of graphs with a strong transience feature called uniform transience. We characterize uniform transience via a Feller-type property and via validity of an…
The Feller Property for Graphs
Radoslaw K. Wojciechowski
The Feller property concerns the preservation of the space of functions vanishing at infinity by the semigroup generated by an operator. We study this property in the case of the L…
Graphs of finite measure
Agelos Georgakopoulos, Sebastian Haeseler, Matthias Keller +2
We consider weighted graphs with an infinite set of vertices. We show that boundedness of all functions of finite energy can be seen as a notion of `relative compactness' for such…
Cheeger inequalities for unbounded graph Laplacians
Frank Bauer, Matthias Keller, Radosław K. Wojciechowski
We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate…
A note on self-adjoint extensions of the Laplacian on weighted graphs
Xueping Huang, Matthias Keller, Jun Masamune +1
We study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on weighted graphs. We first show that, for locally finite graphs and a certain family of metrics,…
Volume growth and bounds for the essential spectrum for Dirichlet forms
Sebastian Haeseler, Matthias Keller, Radosław K. Wojciechowski
We consider operators arising from regular Dirichlet forms with vanishing killing term. We give bounds for the bottom of the (essential) spectrum in terms of exponential volume gro…
Volume Growth, Spectrum and Stochastic Completeness of Infinite Graphs
Matthias Keller, Daniel Lenz, Radoslaw K. Wojciechowski
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…
Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions
Sebastian Haeseler, Matthias Keller, Daniel Lenz +1
We study Laplacians associated to a graph and single out a class of such operators with special regularity properties. In the case of locally finite graphs, this class consists of…
Note on basic features of large time behaviour of heat kernels
Matthias Keller, Daniel Lenz, Hendrik Vogt +1
Large time behaviour of heat semigroups (and more generally, of positive selfadjoint semigroups) is studied. Convergence of the semigroup to the ground state and of averaged logari…
Stochastically Incomplete Manifolds and Graphs
Radoslaw Krzysztof Wojciechowski
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 com…
Heat Kernel and Essential Spectrum of Infinite Graphs
Radoslaw K. Wojciechowski
We study the existence and uniqueness of the heat kernel on infinite, locally finite, connected graphs. For general graphs, a uniqueness criterion, shown to be optimal, is given in…
Stochastic Completeness of Graphs
Radoslaw K. Wojciechowski
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, lo…