Green’s Function of a Subgraph of a Complete Graph

Author:

Lin Yong1,Ngai Sze-Man2,Yau Shing-Tung3

Affiliation:

1. Yau Mathematical Sciences Center, Tsinghua University , Beijing 100084, China, and Department of Mathematics, Tsinghua University, Beijing 100084, China

2. Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China) , College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China, and Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460-8093, USA

3. Department of Mathematics, Harvard University , One Oxford Street, Cambridge, MA 02138, USA, and Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China

Abstract

Abstract By using heat kernel expansions for the Laplacian on a subgraph of a complete graph, we obtain formal expansions for the Green function of the Laplacian on a subgraph of a complete graph. We study this formal series for both the cases that the subgraph is complete and not complete, and in both cases, we obtain precise information about the convergence of the series.

Funder

National Natural Science Foundation of China

Center of Mathematical Sciences and Applications of Harvard University

Construct Program of the Key Discipline in Hunan Province

Georgia Southern University

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

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