We establish existence of Stein kernels for probability measures on R satisfying a Poincaré inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are discussed, including a new CLT in Wasserstein distance W2 with optimal rate and dependence on the dimension. As a byproduct, we obtain a stable version of an estimate of the Po...

We consider the problem to reconstruct a wave speed c ∈ C∞(M) in a domain M ⊂ R from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map Λ. We introduce a reconstruction formula for c that is based on the Boundary Control method and incorporates features also from the complex geometric optics solutions approach. Moreover, we show that the reconstruction formula is...

In recent works by Singer, Douglas and Gopakumar and Gross an application of results of Voiculescu from non-commutative probability theory to constructions of the master field for large N matrix field theories have been suggested. In this note we consider interrelations between the master field and quantum groups. We define the master field algebra and observe that it is isomorphic to the algeb...

In this article, we study the existence of the eigencurves for a Steklov problem and we obtain their variational formulation. Also we prove the simplicity and the isolation results of each point of the principal eigencurve. Also we obtain the continuity and the differentiability of the principal eigencurve.

We introduce a novel and efficient simulation technique for generating physics-based skinning animations of skeleton-driven characters with full support for collision handling. Although physics-based approaches may use a volumetric (e.g. tetrahedral) flesh model, operations such as rendering, collision processing and user manipulation directly involve only the surface of this mesh. Motivated by...

In this paper we find the asymptotic behavior of the spectral counting function for the Steklov problem in a family of self similar domains with fractal boundaries. Using renewal theory, we show that the main term in the asymptotics depends on the Minkowski dimension of the boundary. Also, we compute explicitly a three term expansion for a family of self similar sets, and a two term asymptotic ...

We give an exact analytic solution of the strong coupling limit of the integral equation which was recently proposed to describe the universal scaling function of high spin operators in N = 4 gauge theory. The solution agrees with the prediction from string theory, confirms the earlier numerical analysis and provides a basis for developing a systematic perturbation theory around strong coupling...

We study the nodal set of the Steklov eigenfunctions on the boundary of a smooth bounded domain in Rn – the eigenfunctions of the Dirichlet-to-Neumann map Λ. For a bounded Lipschitz domain Ω ⊂ Rn, this map associates to each function u defined on the boundary ∂Ω, the normal derivative of the harmonic function on Ω with boundary data u. Under the assumption that the domain Ω is C2, we prove a do...