Heat kernels on regular graphs and generalized Ihara zeta function formulas

DOI10.1007/s00605-014-0685-4zbMath1321.05118arXiv1302.4644OpenAlexW1991115567MaRDI QIDQ500314

Anders Karlsson, Gautam Chinta, Jay A. Jorgenson

Publication date: 2 October 2015

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.4644

zbMATH Keywords

regular graphsBessel functionsheat kernelsIhara zeta function

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Other Dirichlet series and zeta functions (11M41) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Heat kernel (35K08)

Related Items

Tree-lattice zeta functions and class numbers ⋮ Two-sided estimates of total bandwidth for Schrödinger operators on periodic graphs ⋮ Ihara Zeta Functions of Infinite Weighted Graphs ⋮ An explicit prime geodesic theorem for discrete tori and the hypergeometric functions ⋮ Vertex-face/zeta correspondence ⋮ Grover/zeta correspondence based on the Konno-Sato theorem ⋮ Discrete time heat kernel and UV modified propagators with dimensional deconstruction ⋮ Discrete diffusion-type equation on regular graphs and its applications ⋮ An Asymptotic Expansion of the Trace of the Heat Kernel of a Singular Two-particle Contact Interaction in One-dimension ⋮ Spectral Zeta Functions ⋮ Zeta functions from graphs ⋮ Convergence of zeta functions for amenable group extensions of shifts ⋮ The Ihara zeta function for infinite graphs ⋮ Invasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erdős-Réyni graphs ⋮ Limiting eigenvalue distribution of random matrices of Ihara zeta function of long-range percolation graphs ⋮ Heat kernels on forms defined on a subgraph of a complete graph ⋮ Trace formulas for Schrödinger operators on periodic graphs ⋮ Transition fronts of Fisher-KPP equations in locally spatially inhomogeneous patchy environments ⋮ A generalized Ihara zeta function formula for simple graphs with bounded degree ⋮ Walk/zeta correspondence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Zeta functions of finite graphs and coverings. III
• Ihara's zeta function for periodic graphs and its approximation in the amenable case
• Coverings, heat kernels and spanning trees
• Selberg's trace formula on the \(k\)-regular tree and applications
• Two-sided bounds uniform in the real argument and the index for modified Bessel functions
• Discrete path integral approach to the Selberg trace formula for regular graphs
• On discrete subgroups of the two by two projective linear group over \(p\)-adic fields
• The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps
• Ihara Zeta Functions of Infinite Weighted Graphs
• Zeta functions, heat kernels, and spectral asymptotics on degenerating families of discrete tori
• Trace formulae and spectral statistics for discrete Laplacians on regular graphs (I)
• A Survey on Spectra of infinite Graphs
• A Combinatorial Proof of Bass’s Evaluations of the Ihara-Selberg Zeta Function for Graphs
• Estimates for functions of the Laplace operator on homogeneous trees
• THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE
• Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝
• Zeta functions of discrete groups acting on trees