Random fractal strings: Their zeta functions, complex dimensions and spectral asymptotics

DOI10.1090/S0002-9947-05-03646-9zbMath1079.60019MaRDI QIDQ5694984

Michel L. Lapidus, Benjamin M. Hambly

Publication date: 6 October 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

branching processstable subordinatorrandom recursive fractal

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Other Dirichlet series and zeta functions (11M41) Fractals (28A80) Stable stochastic processes (60G52) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (12)

Fractal strings and multifractal zeta functions ⋮ Towards zeta functions and complex dimensions of multifractals ⋮ Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis ⋮ Central limit theorems for the spectra of classes of random fractals ⋮ Truncated infinitesimal shifts, spectral operators and quantized universality of the Riemann zeta function ⋮ Distance and tube zeta functions of fractals and arbitrary compact sets ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Tube formulas and complex dimensions of self-similar tilings ⋮ A probabilistic analysis of some tree algorithms ⋮ The Sound of Fractal Strings and the Riemann Hypothesis ⋮ Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back

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