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Brownian Motions on Metric Graphs

Probability 2015-05-27 v3

Abstract

Brownian motions on a metric graph are defined. Their generators are characterized as Laplace operators subject to Wentzell boundary at every vertex. Conversely, given a set of Wentzell boundary conditions at the vertices of a metric graph, a Brownian motion is constructed pathwise on this graph so that its generator satisfies the given boundary conditions.

Keywords

Cite

@article{arxiv.1102.4937,
  title  = {Brownian Motions on Metric Graphs},
  author = {Vadim Kostrykin and Jürgen Potthoff and Robert Schrader},
  journal= {arXiv preprint arXiv:1102.4937},
  year   = {2015}
}

Comments

43 pages, 7 figures. 2nd revision of our article 1102.4937: The introduction has been modified, several references were added. This article will appear in the special issue of Journal of Mathematical Physics celebrating Elliott Lieb's 80th birthday

R2 v1 2026-06-21T17:31:02.455Z