[图书][B] Graphs and discrete Dirichlet spaces
The present book deals with the spectral geometry of infinite graphs. This topic involves the
interplay of three different subjects: geometry, the spectral theory of Laplacians and the heat …
interplay of three different subjects: geometry, the spectral theory of Laplacians and the heat …
Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature
RK Wojciechowski - Journal of Fourier Analysis and Applications, 2021 - Springer
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 …
graphs. In particular, we present a variety of formulations of stochastic completeness and …
A non-linear characterization of stochastic completeness of graphs
M Schmidt, I Zimmermann - arXiv preprint arXiv:2403.15125, 2024 - arxiv.org
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 …
solutions to corresponding semi-linear elliptic equations and use them to introduce the …
Explosion by Killing and Maximum Principle in Symmetric Markov Processes
M Takeda - arXiv preprint arXiv:2406.15974, 2024 - arxiv.org
Keller and Lenz\cite {KL} define a concept of {\it stochastic completeness at infinity}(SCI) for
a regular symmetric Dirichlet form $(\cE,\cF) $. We show that (SCI) can be characterized …
a regular symmetric Dirichlet form $(\cE,\cF) $. We show that (SCI) can be characterized …