Analysis of the physical Laplacian and the heat flow on a locally finite graph

By Andreas Weber. 2008

116 citations recorded by the source corpus.

We study the physical Laplacian and the corresponding heat flow on an infinite, locally finite graph with possibly unbounded valence.

Subfields: Computational Theory and Mathematics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/873b9d229e35efbdc3e8be2df0e533d9b0493b12

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In Computational Theory and Mathematics

In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Volume growth and stochastic completeness of graphs (2012, background): “For analytic properties of the operator L X , which is sometimes referred to as the physical Laplacian, see [33].”
Dirichlet forms and stochastic completeness of graphs and subgraphs (2009, unknown): “Our setting generalizes the setting of [9], [11], [17], [26], [28] to Dirichlet forms on countable sets.”
Heat Kernel and Essential Spectrum of Infinite Graphs (2008, unknown): “27 45 v4 [ m at h. SP ] 2 4 A pr 2”
Volume growth, spectrum and stochastic completeness of infinite graphs (2011, methodology): “We refer to these quantities as curvatures as, for c ≡ 0, L̃d(x0, ·) = κ−(·) − κ+(·) is often referred to as a curvature-type quantity for graphs, see [17, 33,54].”
On the conservativeness and the recurrence of symmetric jump-diffusions (2012, background): “The conservativeness of the process associated with the physical Laplacian was studied in [6,7,39,40,15].”
Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation (2011, methodology): “This has been shown in [22] in our setting after earlier results in [8, 32, 33] for locally finite graphs.”
A note on self-adjoint extensions of the Laplacian on weighted graphs (2012, background): “More specifically, this problem is studied for adjacency, (magnetic) Laplacian, and Schrödinger-type operators on graphs in [4, 5, 6, 16, 17, 18, 23, 27, 28, 30, 31, 34, 37, 39, 40, 42, 43, 44, 45] among others.”
Gaussian Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks (2011, methodology): “We discuss here an alternative construction of the heat kernel which will be used in Section 3; this closely follows the discussion in [25].”