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MONTE CARLO SAMPLING IN DUAL SPACE FOR APPROXIMATING THE EMPIRICAL HALFSPACE DISTANCE
SPACE FOR APPROXIMATING EMPIRICAL HALFSPACE DISTANCE
2015/8/20
The Kolmogorov]Smirnov distance is an important tool for constructing confidence sets and tests in univariate problems. In multivariate
settings, an analogous role is played by the halfspace di...
Approximations of convex bodies by polytopes and by projections of spectrahedra
convex body spectrahedron approximation computational complex-ity semidefinite programming
2012/4/18
We prove that for any compact set B in R^d and for any epsilon >0 there is a finite subset X of B of |X|=d^{O(1/epsilon^2)} points such that the maximum absolute value of any linear function ell: R^d ...
Hilbert's Tenth Problem and Mazur's Conjectures in Complementary Subrings of Number Fields
Hilbert’s Tenth Problem undecidability elliptic curves primitive divisor
2011/2/24
We show that Hilbert’s Tenth Problem is undecidable for complementary subrings of number fields and that the p-adic and archimedean ring versions of Mazur’s conjectures do not hold in these rings .
Central limit theorems for Hilbert-space valued random fields satisfying a strong mixing condition
Central limit theorems Hilbert-space valued
2011/1/19
In this paper we study the asymptotic normality of the normalized partial sum of a Hilbert-space valued strictly stationary random field satisfying the interlaced ρ′-mixing condition.
Hilbert-Kunz theory for nodal cubics, via sheaves
Hilbert-Kunz theory nodal cubics sheaves
2011/1/20
Suppose B = F[x, y, z]/h is the homogeneous coordinate ring of a characteristic p degree 3 irreducible plane curve C with a node. Let J be a homogeneous (x, y, z)-primary ideal and n → en be the Hilbe...
On the Hilbert scheme of determinantal subvarieties
Determinantal subvariety Maximal minors Hilbert scheme Projective bundle
2011/2/24
We compute the dimension of the Hilbert scheme of subvarieties of positive dimension in projective space which are defined as vanishing loci of maximal minors of a matrix with polynomial entries.
Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space
Real analytic approximations Lipschitz constants of functions defined Hilbert space
2011/2/24
Let X be a separable real Hilbert space. We show that for every Lipschitz function f : X ! R, and for every " > 0, there exists a Lipschitz, real analytic function g : X ! R such that |f(x) − g(...
Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces
Exchange perverse weight filtration Hilbert schemes points of two surfaces
2011/1/21
We show that a natural isomorphism between the rational cohomology groups of the two zero-dimensional Hilbert schemes of n-points of two surfaces, the affine plane minus the axes and the cotangent bun...
Relative trace formulae toward Bessel and Fourier-Jacobi periods of unitary groups
Relative trace formulae Fourier-Jacobi periods of unitary groups
2011/2/24
We propose a relative trace formula approach and state the corresponding fundamental lemma
toward the global restriction problem involving Bessel or Fourier-Jacobi periods of unitary groups Un×Um, ex...
A period differential equation for a family of $K3$ surfaces and the Hilbert modular orbifold for the field $\mathbb{Q}(\sqrt{5})$
K3 surfaces Hilbert modular orbifolds period maps period di erential equations toric varieties
2010/12/14
In this article we study the period map for a family of K3 surfaces which is given by the anticanon-ial divisor of a toric variety. We determine the period di erential equation and its monodromy group...
For a smooth projective variety P, we construct a Cartier divisor supported on the incidence locus in Ca(P) × Cdim(P)−a−1(P). There is a natural definition of the corresponding line bundle...
Non-coherent Components of the Toric Hilbert Scheme
Non-coherent Components Toric Hilbert Scheme
2010/12/9
We want to understand the geometry of all irreducible components of the toric Hilbert scheme. Until now it is known that the coherent component is (up to normalisation)the toric variety associated to ...
Asymptotic normality of Hill Estimator for truncated data
heavy tails truncation second order regular variation
2010/12/9
The problem of estimating the tail index from truncated data is addressed in Chakrabarty and Samorodnitsky (2009). In that paper, a sample based (and hence random) choice of k is uggested,and it is sh...
Heisenberg categorification and Hilbert schemes
Heisenberg categorification Hilbert schemes
2010/12/13
Given a finite subgroup SL2(C) we define an additive 2-category H whose Grothendieck
group is isomorphic to an integral form h of the Heisenberg algebra. We construct...
Let Q = P1 × P1 and let X Q be a 0-dimensional scheme. This paper is a first step towards the characterization of Hilbert functions of 0-dimensional schemes in Q. In particular we show how, under so...