Brownian motion and the fundamental frequency of a drum
type: Item
instance of: scholarly article
title: Brownian motion and the fundamental frequency of a drum
zbMATH Open document ID: 0817.58046
DOI: 10.1215/S0012-7094-94-07517-0
author: Rodrigo Bañuelos
author: Tom Carroll
published in: Duke Mathematical Journal
publication date: 1995-01-02T00:00:00Z
review text: Let \(\lambda_ D\) be the first Dirichlet eigenvalue for the Laplacian in the simply connected domain \(D\). Let \(\tau_ D\) be the first exit time of the Brownian motion from \(D\) and \(E_ z(\tau_ D)\) be the expectation of \(\tau_ D\) under the measure of this Brownian motion starting at the point \(z\) in \(D\). Some estimates for the eigenvalue \(\lambda_ D\) and for the expectation \(E_ z(\tau_ D)\) are established.
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 706698
zbMATH Keywords: first Dirichlet eigenvalue
zbMATH Keywords: Laplacian
zbMATH Keywords: exit time
zbMATH Keywords: Brownian motion
reviewed by: Simon Eloshvili
MaRDI profile type: Publication
cites work: On Strong Barriers and an Inequality of Hardy for Domains in R n
cites work: Q3876353
cites work: Exit times for elliptic diffusions and BMO
cites work: Conditioned Brownian motion and hyperbolic geodesics in simply connected domains
cites work: On the univalent bloch constant
cites work: The First Eigenvalue of the Laplacian for Plane Domains
cites work: Q3217388
cites work: On the Bloch-Landau constant for schlicht functions
cites work: Brownian motion and eigenvalues for the Dirichlet Laplacian
cites work: Some bounds for principal frequency
cites work: Q4692700
cites work: Sur la frequence fondamentale d'une membrane vibrante: evaluations par defaut et principe de maximum
cites work: Q3286467
cites work: A criterion associated with the schlicht Bloch constant
cites work: Lower bounds for the hyperbolic metric in convex regions
cites work: A note on Hayman's theorem on the bass note of a drum
cites work: Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function
cites work: Isoperimetric Inequalities in Mathematical Physics. (AM-27)
cites work: The Bloch constant 𝔄 for a schlicht function
cites work: Maximum principles and their applications
cites work: Estimate on the fundamental frequency of a drum
cites work: Q4712975
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description: scientific article; zbMATH DE number 706698