Related papers: Conformal capacity and polycircular domains
We study the condenser capacity $\mathrm{cap}_p(E,\Omega)$ on \emph{unbounded} open sets $\Omega$ in a proper connected metric space $X$ equipped with a locally doubling measure supporting a local $p$-Poincar\'e inequality, where…
We solve the classical conformal welding problem for a composition of two random homeomorphisms generated by independent Gaussian multiplicative chaos measures with small parameter values. In other words, given two such measures on the…
In this article, we survey the primary research on polyhedral computing methods for constrained linear control systems. Our focus is on the modeling power of convex optimization, featured to design set-based robust and optimal controllers.…
Under some general assumptions, we construct the scaling limit of open clusters and their associated counting measures in a class of two dimensional percolation models. Our results apply, in particular, to critical Bernoulli site…
We find an asymptotic formula for the conformal capacity of a plane condenser both plate of which are concentric circular arcs as the distance between them vanishes. This result generalizes the formula for the capacity of parallel linear…
We review some important ideas in the design and analysis of robust overlapping domain decomposition algorithms for high-contrast multiscale problems and propose a domain decomposition method better performance in terms of the number of…
This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…
We study asymptotic behaviors near the boundary of complete metrics of constant curvature in planar singular domains and establish an optimal estimate of these metrics by the corresponding metrics in tangent cones near isolated singular…
We compute $M$-point conformal blocks with scalar external and exchange operators in the so-called comb configuration for any $M$ in any dimension $d$. Our computation involves repeated use of the operator product expansion to increase the…
We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…
It is common in machine learning to estimate a response $y$ given covariate information $x$. However, these predictions alone do not quantify any uncertainty associated with said predictions. One way to overcome this deficiency is with…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
We study a scaling limit associated to a model of planar aggregation. The model is obtained by composing certain independent random conformal maps. The evolution of harmonic measure on the boundary of the cluster is shown to converge to the…
We consider two different versions of the double dimer model on a planar domain, where we either fold a single dimer cover on a symmetric domain onto itself across the line of symmetry, or we superimpose two independent dimer covers on two,…
When a convex perfectly conducting inclusion is closely spaced to the boundary of the matrix domain, a bigger convex domain containing the inclusion, the electric field can be arbitrary large. We establish both the pointwise upper bound and…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
In the optimization of convex domains under a PDE constraint numerical difficulties arise in the approximation of convex domains in $\mathbb{R}^3$. Previous research used a restriction to rotationally symmetric domains to reduce shape…
In numerical simulations a smooth domain occupied by a fluid has to be approximated by a computational domain that typically does not coincide with a physical domain. Consequently, in order to study convergence and error estimates of a…
Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…