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math-phSep 9, 2006
32
citations (OpenAlex)
authors
  • Pavel Mnev
institutions
  • St. Petersburg Department of Steklov Institute of Mathematics
arXiv abstractPDF
paper

Discrete path integral approach to the trace formula for regular graphs

arXiv:math-ph/0609028 · doi:10.1007/s00220-007-0257-8

Abstract

We give a new proof of the trace formula for regular graphs. Our approach is inspired by path integral approach in quantum mechanics, and calculations are mostly combinatorial.

8 pages, no figures

Cited by in corpus (12)

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  • Hyperwalk Formulae for Even and Odd Laplacians in Finite CW-Hypergraphs
  • Walking on Archimedean Lattices: Insights from Bloch Band Theory
  • Super-Walk Formulae for Even and Odd Laplacians in Finite Graphs
  • Lattice sums of I-Bessel functions, theta functions, linear codes and heat equations
  • Graph-theory induced gravity and strongly-degenerate fermions in a self-consistent Einstein universe
  • Graph de Rham Cohomology and the Automorphsim Group
  • Heat kernels on regular graphs and generalized Ihara zeta function formulas
  • The limit theorem with respect to the matrices on non-backtracking paths of a graph
  • Clustering of spectra and fractals of regular graphs
  • Gluing of Graph Laplacians and Their Spectra
  • Periodic Walks on Large Regular Graphs and Random Matrix Theory
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