16 citations · 43 across the 8 of their papers we have counts for
9 papers
Localization of Neumann Eigenfunctions near Irregular Boundaries
Peter W. Jones, Stefan Steinerberger
It has been empirically observed that eigenfunctions of Laplace's equation with Neumann boundary conditions sometimes localize near the boundary of the domain if that bou…
Product Formalisms for Measures on Spaces with Binary Tree Structures: Representation, Visualization, and Multiscale Noise
Devasis Bassu, Peter W. Jones, Linda Ness +1
In this paper we present a theoretical foundation for a representation of a data set as a measure in a very large hierarchically parametrized family of positive measures, whose par…
A Multiscale Guide to Brownian Motion
Denis S. Grebenkov, Dmitry Beliaev, Peter W. Jones
We revise the Levy's construction of Brownian motion as a simple though still rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructe…
Metric properties of mean wiggly continua
Jacek Graczyk, Peter W. Jones, Nicolae Mihalache
We study lower and upper bounds of the Hausdorff dimension for sets which are wiggly at scales of positive density. The main technical ingredient is a construction, for every conti…
Random Conformal Weldings
K. Astala, P. Jones, A. Kupiainen +1
We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle. The homeomorphism is constructed using the…
Universal local parametrizations via heat kernels and eigenfunctions of the Laplacian
Peter W. Jones, Mauro Maggioni, Raanan Schul
We use heat kernels or eigenfunctions of the Laplacian to construct local coordinates on large classes of Euclidean domains and Riemannian manifolds (not necessarily smooth, e.g. w…