Related papers: Interpolation percolation
Using polynomial interpolation, along with structural properties of the family of positive real rational functions, we here show that a set of m nodes in the open left half of the complex plane, can always be mapped to anywhere in the…
There are various situations in which it is natural to ask whether a given collection of $k$ functions, $\rho_j(\r_1,...,\r_j)$, $j=1,...,k$, defined on a set $X$, are the first $k$ correlation functions of a point process on $X$. Here we…
We introduce the notion of almost realizability, an arithmetic generalization of realizability for integer sequences, which is the property of counting periodic points for some map. We characterize the intersection between the set of…
We consider a type of long-range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word…
We consider conditions for the convergence of sequences in terms of positive and alternating Perron expansions ($P$-representation and $P^-$-representation). These conditions are crucial to determine the continuity of functions that are…
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…
The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed…
We treat the interpolation problem $ \{f(x_j)=y_j\}_{j=1}^N $ for polynomial and rational functions. Developing the approach by C.Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences $…
We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…
We study uniform interpolation and forgetting in the description logic ALC. Our main results are model-theoretic characterizations of uniform inter- polants and their existence in terms of bisimula- tions, tight complexity bounds for…
Let $\mathcal{I}$ be an analytic P-ideal [respectively, a summable ideal] on the positive integers and let $(x_n)$ be a sequence taking values in a metric space $X$. First, it is shown that the set of ideal limit points of $(x_n)$ is an…
We consider quantum interpolation of polynomials. We imagine a quantum computer with black-box access to input/output pairs (x_i, f(x_i)), where f is a degree-d polynomial, and we wish to compute f(0). We give asymptotically tight quantum…
We consider the Boolean model with random radii based on Cox point processes. Under a condition of stabilization for the random environment, we establish existence and non-existence of subcritical regimes for the size of the cluster at the…
The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of $[0,1]^n$. We take this basic fact as a starting point to define the Choquet integral in a very general way,…
An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar…
Limiting real interpolation method is applied to describe the behaviour of the Fourier coefficients of functions that belong to spaces which are "very close" to L2.
For some m \ge 4, let us color each column of the integer lattice L = Z^2 independently and uniformly into one of m colors. We do the same for the rows, independently from the columns. A point of L will be called blocked if its row and…
Let $f$ be a $r\times m$-matrix of holomorphic functions that is generically surjective. We provide explicit integral representation of holomorphic $\psi$ such that $\phi=f\psi$, provided that $\phi$ is holomorphic and annihilates a certain…
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…
We construct families of rational functions $f \colon \bP^1_k \to \bP^1_k$ of degree $d \geq 2$ over a perfect field $k$ whose associated fixed-point processes fail to be martingales. Conversely, for any normal variety $X \subset…