Related papers: Explicit examples in Ergodic Optimization
We study the heterotic string compactified on K3 x T^2 near the line T=U, where the effective action becomes singular due to an SU(2) gauge symmetry enhancement. By `integrating in' the light W^\pm vector multiplets we derive a quantum…
We consider a piecewise analytic expanding map f: [0,1]-> [0,1] of degree d which preserves orientation, and an analytic positive potential g: [0,1] -> R. We address the analysis of the following problem: for a given analytic potential beta…
In this short and elementary note, we study some ergodic optimization problems for circle expanding maps. We first make an observation that if a function is not far from being convex, then its calibrated sub-actions are closer to convex…
Consider a lattice $\Gamma$ in a group $G = SL_2(\R), SO(1,n), SU(1,n)$, $SL_2(\Q_p)$. We discuss actions of $\Gamma$ by affine isometric transformations of Hilbert spaces. We show that for irreducible affine isometric action of $G$ its…
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
Let C/K be a curve over a local field. We study the natural semilinear action of Galois on the minimal regular model of C over a field F where it becomes semistable. This allows us to describe the Galois action on the l-adic Tate module of…
The matrix $A:\mathbb{R}^n \to \mathbb{R}^m$ is $(\delta,k)$-regular if for any $k$-sparse vector $x$, $$ \left| \|Ax\|_2^2-\|x\|_2^2\right| \leq \delta \sqrt{k} \|x\|_2^2. $$ We show that if $A$ is $(\delta,k)$-regular for $1 \leq k \leq…
The calculation of the effective potential for fixed-end and toroidal rigid $p$-branes is performed in the one-loop as well as in the $1/d$ approximations. The analysis of the involved zeta-functions (of inhomogeneous Epstein type) which…
We prove long variational estimates for the bilinear ergodic averages \[ A_{N;X}(f,g)(x) = \frac{1}{N} \sum_{n=1}^N f(T^{\lfloor \sqrt{n} \rfloor}x) g(T^nx) \] on an arbitrary measure preserving system $(X,\mu,T)$ for the full expected…
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…
A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding…
We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring…
In 1973 V.L.Popov classified affine SL(2)-embeddings. He proved that a locally transitive SL(2)-action on a normal affine three-dimensional variety X is uniquely determined by a pair (p/q, r), where 0<p/q<=1 is an uncancelled fraction and r…
We obtain a closed form effective potential at the one-loop level of a Two Higgs Doublet Model. Through the loop expansion we reproduce the expression presented by Weinberg and Coleman, showing explicitly every step involved in the…
We consider the proximal-gradient method for minimizing an objective function that is the sum of a smooth function and a non-smooth convex function. A feature that distinguishes our work from most in the literature is that we assume that…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
We analyze a fixed-point iteration $v \leftarrow \phi(v)$ arising in the optimization of a regularized nuclear norm objective involving the Hadamard product structure, posed in DMR+22 in the context of an optimization problem over the space…
We introduce sufficient conditions on discrete singular integral operators for their maximal truncations to satisfy a sparse bound. The latter imply a range of quantitative weighted inequalities, which are new. As an application, we prove…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
In this paper, we present a thorough study of maximizing a regularized non-monotone submodular function subject to various constraints, i.e., $\max \{ g(A) - \ell(A) : A \in \mathcal{F} \}$, where $g \colon 2^\Omega \to \mathbb{R}_+$ is a…