A connection between discrete and regularized Laplacian determinants on fractals

Fractals (28A80) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Cites Work

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Spectral analysis on infinite Sierpiński fractafolds
Existence of a meromorphic extension of spectral zeta functions on fractals
Ten physical applications of spectral zeta functions.
The number of spanning trees in self-similar graphs
On eigenvalue problems for the random walks on the Sierpinski pre- gaskets
On a spectral analysis for the Sierpiński gasket.
Laplacians on the basilica Julia set
Zeta function regularization of path integrals in curved spacetime
Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
Self-similarity, operators and dynamics
Regularized Laplacian determinants of self-similar fractals
Regularized limit of determinants for discrete tori
On eigenvalue problems for Laplacians on p.c.f. self-similar sets
Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice.
Approximation of fractals by discrete graphs: norm resolvent and spectral convergence
Spectral decimation for a graph-directed fractal pair
Fractal space-times under the microscope: a renormalization group view on Monte Carlo data
Enumeration problems for classes of self-similar graphs
Exact spectrum of the Laplacian on a domain in the Sierpinski gasket
Analysis on fractals
Singularly continuous spectrum of a self-similar Laplacian on the half-line
Counting spanning trees on fractal graphs and their asymptotic complexity
The statistics of dimers on a lattice
Heat kernels and zeta functions on fractals
Statistical Mechanics and Quantum Fields on Fractals
Laplace operators on fractals and related functional equations
Spectral zeta functions of fractals and the complex dynamics of polynomials
Spectral dimension and Bohr's formula for Schrödinger operators on unbounded fractal spaces
Zeta functions, heat kernels, and spectral asymptotics on degenerating families of discrete tori
Fractafolds based on the Sierpinski gasket and their spectra
Exact spectral asymptotics on the Sierpinski gasket
The zeta function of the Laplacian on certain fractals
Vibration modes of 3n-gaskets and other fractals
Asymptotic Enumeration of Spanning Trees

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