Related papers: Inverting Ray-Knight identity
We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyans theorem.
This note contains two remarks. The first remark concerns the extension of the well-known Cayley representation of rotation matrices by skew symmetric matrices to rotation matrices admitting -1 as an eigenvalue and then to all orthogonal…
In this paper we consider the generalized Radon transform $\mathcal R$ in the plane. Let $f$ be a piecewise smooth function, which has a jump across a smooth curve $\mathcal S$. We obtain a formula, which accurately describes view aliasing…
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and non irreducible Markov chains…
We present a proof of Roth's theorem that follows a slightly different structure to the usual proofs, in that there is not much iteration. Although our proof works using a type of density increment argument (which is typical of most proofs…
The Central Limit Theorem for the random walk on a stationary random network of conductances has been studied by several authors. In one dimension, when conductances and resistances are integrable, and following a method of martingale…
We study the existence and the number of $k$-neighborly reorientations of an oriented matroid. This leads to $k$-variants of McMullen's problem and Roudneff's conjecture, the case $k=1$ being the original statements on complete cells in…
In this paper, we consider the quenched invariance principle for random Young towers driven by an ergodic system. In particular, we obtain the Wassertein convergence rate in the quenched invariance principle. As a key ingredient, we derive…
The standard General Relativity results for precession of particle orbits and for bending of null rays are derived as special cases of perturbation of a quantity that is conserved in Newtonian physics, the Runge-Lenz vector. First this…
While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…
In the present article we consider the uniqueness problem for the generalized Radon transform arising in a mathematical model of production. We prove uniqueness theorems for this transform and for the profit function in the corresponding…
We introduce and study in detail a special class of backward continued fractions that represents a generalization of R\'enyi continued fractions. We investigate the main metrical properties of the digits occurring in these expansions and we…
A version of Radon-Nikodym theorem for the Choquet integral w.r.t. monotone measures is proved. Without any presumptive condition, we obtain a necessary and sufficient condition for the ordered pair $(\mu, \nu)$ of finite monotone measures…
We consider the problem of testing the identity of a reversible Markov chain against a reference from a single trajectory of observations. Employing the recently introduced notion of a lumping-congruent Markov embedding, we show that, at…
An example of full solution of the inverse scattering problem on the half line is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a…
We establish annealed and quenched invariance principles for random walks in random conductances lifted to the p-variation rough path topology, allowing for degenerate environments and long-range jumps. Our proof is based on a unified…
This paper gives some further details of proofs of some theorems related to the quantum dynamical Yang-Baxter equation. This mainly expands proofs given in "Lectures on the dynamical Yang-Baxter equation" by P. Etingof and O. Schiffmann,…
In this article we focus on a general model of random walk on random marked trees. We prove a recurrence criterion, analogue to the recurrence criterion proved by R. Lyons and Robin Pemantle (1992) in a slightly different model. In the…
The windowed ray transform is a natural generalization of the "Analytic-Signal Transform" which is developed to extend arbitrary functions from $\RR^n$ to $\CC^n$. We present several inversion formulas here.
We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral…