Related papers: Convergence of multipole Green functions

For a chordal SLE$_\kappa$ ($\kappa\in(0,8)$) curve in a domain $D$, the $n$-point Green's function valued at distinct points $z_1,\dots,z_n\in D$ is defined to be $$G(z_1,\dots,z_n)=\lim_{r_1,\dots,r_n\downarrow 0} \prod_{k=1}^n r_k^{d-2}…

In this paper we introduce a weak version of level and epigraph convergence for level functions on topological spaces. In the particular case of topological groups we are able to define convolutions in the set of level functions and show…

We show a new functional limit theorem for weakly dependent regularly varying sequences of random vectors. As it turns out, the convergence takes place in the space of R^d valued c\`{a}dl\`{a}g functions endowed with the so-called weak M1…

We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness,…

We extend certain classical theorems in pluripotential theory to a class of functions defined on the support of a $(1,1)$-closed positive current $T$, analogous to plurisubharmonic functions, called $T$-plurisubharmonic functions. These…

We study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and $L^2$-cohomology of the capacity metric and…

We show how few-particle Green's functions can be calculated efficiently for models with nearest-neighbor hopping, for infinite lattices in any dimension. As an example, for one dimensional spinless fermions with both nearest-neighbor and…

We study inequalities for the infima of Green potentials on a compact subset of an arbitrary domain in the complex plane. The results are based on a new representation of the pseudohyperbolic farthest-point distance function via a Green…

Given a compact K\"ahler manifold $X$, a quasiplurisubharmonic function is called a Green function with pole at $p\in X$ if its Monge-Amp\`ere measure is supported at $p$. We study in this paper the existence and properties of such…

We prove compactness with respect to $\Gamma$-convergence for a general class of non-local energies modelled after the ones considered in [Gobbino, CPAM (1998)]. We give an integral representation result for the limits, which are free…

We study integral functionals constrained to divergence-free vector fields in $L^p$ on a thin domain, under standard $p$-growth and coercivity assumptions, $1<p<\infty$. We prove that as the thickness of the domain goes to zero, the…

We show that, under mild assumptions on the limiting curve, a sequence of simple chordal planar curves converges uniformly whenever certain Loewner driving functions converge. We extend this result to random curves. The random version…

We investigate a new property of retarded Green's functions using AdS/CFT. The Green's functions are not unique at special points in complex momentum space. This arises because there is no unique incoming mode at the horizon and is similar…

In this article, the Green function for the Stokes flow in the interior, exterior, and annular regions bounded by cylindrical walls is derived as a function of the pole position and expressed invariantly both at the field and pole points.…

Les fonctions plurisousharmoniques negatives dans un domaine D de \CC^n forment un cone convexe. Nous considerons les points extremaux de ce cone, et donnons trois exemples. En particulier, nous traitons le cas de la fonction de Green…

We study the existence of the Green function for an elliptic system in divergence form $-\nabla\cdot a\nabla$ in $\mathbb{R}^d$, with $d>2$. The tensor field $a=a(x)$ is only assumed to be bounded and $\lambda$-coercive. For almost every…

For a strictly stationary sequence of random variables we derive functional convergence of the joint partial sum and partial maxima process under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The…

A Green's function method is developed for solving strongly-coupled gravity and matter in the semiclassical limit. In the strong-coupling limit, one assumes that Newton's constant approaches infinity. As a result, one may neglect second…

Let f be holomorphically continuable over the complex plane except for finitely many branch points contained in the unit disk. We prove that best rational approximants to f of degree n, in the L^2-sense on the unit circle, have poles that…

Our interest is the behavior of weak geodesics between two plurisubharmonic functions on pseudoconvex domains. We characterize the convergence condition along the geodesic between toric psh functions with a pole at origin on a unit ball in…