Related papers: Discretisation for odd quadratic twists
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
In this paper, we study some cohomology groups and quadratic twists of elliptic curves, and apply Tate local duality and the results of Kramer-Tunnell on local norm cokernel to give a refined version of Yu's formula in the case of elliptic…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
The recently proposed differential homotopy approach to the analysis of nonlinear higher spin theory is developed. The Ansatz is extended to the form applicable in the second order of the perturbation theory and general star-multiplication…
Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…
Understanding the continuum limit of a theory of discrete random geometries is a beautiful but difficult challenge. In this optic, we review here the insights that can be obtained for Causal Dynamical Triangulations (CDT) by employing the…
A discretisation scheme for differential geometry is applied to the problem of constructing lattice actions, the naive and staggered action are thus derived. It is found that after specifying an ansatz for the space of fields, the…
We show that some hard to detect properties of quadratic ODEs (eg certain preserved integrals and measures) can be deduced more or less algorithmically from their Kahan discretization, using Darboux Polynomials (DPs). Somewhat similar…
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…
Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, contrary to small deviationresults. In this note we present a novel application of a smalldeviations inequality to a problem related to the diameters of…
We study a discrete variant of the Airy equation, formulated as an advance-delay equation, to reveal that discretization induces the higher-order Stokes phenomenon, which is not present in the continuous Airy function and is typically only…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
We study a special class of non-convex quadratic programs subject to two (possibly indefinite) quadratic constraints when the level sets of the constraint functions are {\it not} arranged {\it alternatively.} It is shown in the paper that…
We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…
We study the second order twist corrections to a toy model of a dipole-dipole interaction in the context of a both deterministic and stochastic effects. This work is done in the high $N_C$ limit in the Bjorken picture. We show that the…
Dyadic shifts of point distributions in the multi-dimensional unit cube are considered as a randomization. Explicit formulas for the discrepancies of such randomized distributions are given in the paper in terms of Rademacher functions.…
I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…