Central limit theorems for the spectra of classes of random fractals

DOI10.1090/tran/7147zbMath1404.28008arXiv1503.06028OpenAlexW2560850102MaRDI QIDQ5367107

Philippe H. A. Charmoy, Benjamin M. Hambly, David A. Croydon

Publication date: 12 October 2017

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

Full work available at URL: https://arxiv.org/abs/1503.06028

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Fractals (28A80) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (1)

A probabilistic model for interfaces in a martensitic phase transition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral asymptotics for stable trees
• On the renewal equation
• Limit theorems for sums determined by branching and other exponentially growing processes
• On a spectral analysis for the Sierpiński gasket.
• Statistically self-similar fractals
• Can one hear the dimension of a fractal?
• A sharp asymptotic remainder estimate for the eigenvalues of the Laplacian in a domain of \(R^3\)
• Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
• Recursive self-similarity for random trees, random triangulations and Brownian excursion
• On the asymptotics of the eigenvalue counting function for random recursive Sierpinski gaskets
• Probabilistic and fractal aspects of Lévy trees
• Harmonic calculus on limits of networks and its application to dendrites
• The continuum random tree. III
• Volume growth and heat kernel estimates for the continuum random tree
• Self-similarity and spectral asymptotics for the continuum random tree
• Fractal Geometry, Complex Dimensions and Zeta Functions
• Random Recursive Constructions: Asymptotic Geometric and Topological Properties
• The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums
• An Estimate Near the Boundary for the Spectral Function of the Laplace Operator
• On the convergence of supercritical general (C-M-J) branching processes
• Meillieurs estimations asymptotiques des restes de la fonctionn spectrale et des valeurs propres relatifs au laplacien.
• Fractal Drum, Inverse Spectral Problems for Elliptic Operators and a Partial Resolution of the Weyl-Berry Conjecture
• One cannot hear the shape of a drum
• On single- and multi-type general age-dependent branching processes
• Localized Eigenfunctions of the Laplacian on p.c.f. Self-Similar Sets
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• On the lattice case of an almost-sure renewal theorem for branching random walks
• Some planar isospectral domains
• Spectral Asymptotics, Renewal Theorem, and the Berry Conjecture for a Class of Fractals
• Counterexamples to the modified Weyl–Berry conjecture on fractal drums
• EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS
• Bounds on the error in the linear approximation to the renewal function
• On Characteristic Functions and Renewal Theory
• On Moment Generating Functions and Renewal Theory
• Can One Hear the Shape of a Drum?
• A limit theorem for a class of supercritical branching processes
• Random fractal strings: Their zeta functions, complex dimensions and spectral asymptotics
• Probability

This page was built for publication: Central limit theorems for the spectra of classes of random fractals