Related papers: Locally-smeared operator product expansions

Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly…

In logarithmic conformal field theory, primary fields come together with logarithmic partner fields on which the stress-energy tensor acts non-diagonally. Exploiting this fact and global conformal invariance of two- and three-point…

We investigate operator delocalization in disordered one-dimensional spin chains by introducing -- besides the already known operator mass -- a complementary measure of operator complexity: the operator length. Like the operator…

We study defects in non-relativistic conformal field theories. As in the well-studied case of relativistic conformal defects, we find that a useful tool to organize correlation functions is the defect operator expansion (dOPE). We analyze…

We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be…

In this article, we propose a shape optimization algorithm which is able to handle large deformations while maintaining a high level of mesh quality. Based on the method of mappings we introduce a nonlinear extension operator, which links a…

Diffusion-based policies have established a new standard for precise robotic manipulation but face a critical scalability bottleneck: high-performance models are computationally expensive, while lightweight alternatives often fail to…

We derive how to incorporate topological features of Riemann surfaces in string amplitudes by insertions of bi-local operators called handle operators. The resulting formalism is exact and globally well-defined in moduli space. After a…

Autonomous exploration in unknown environments is key for mobile robots, helping them perceive, map, and make decisions in complex areas. However, current methods often rely on frequent global optimization, suffering from high computational…

In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems,…

Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…

Mixture-of-Experts (MoE) architectures scale Large Language Models via expert specialization induced by conditional computation. In practice, however, expert specialization often fails: some experts become functionally similar, while others…

The integrable quantum models, associated to the transfer matrices of the 6-vertex reflection algebra for spin 1/2 representations, are studied in this paper. In the framework of Sklyanin's quantum separation of variables (SOV), we provide…

It has been shown recently that the mathematical status of the operator product expansion (OPE) is better than was expected before: namely considering massive Euclidean $\varphi^4$-theory in the perturbative loop expansion, the OPE…

Smooth pseudodifferential operators on $\mathbb{R}^n$ can be characterized by their mapping properties between $L^p-$Sobolev spaces due to Beals and Ueberberg. In applications such a characterization would also be useful in the non-smooth…

We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central role in modeling complex physical systems under…

In this thesis an iterative scheme for the construction of operator product expansion (OPE) coefficients is applied to determine low order coefficients in perturbation theory for a specific toy model. We use the approach to quantum field…

Finding an approximate second-order stationary point (SOSP) is a well-studied and fundamental problem in stochastic nonconvex optimization with many applications in machine learning. However, this problem is poorly understood in the…

We study the operator product expansion (OPE) limit of correlation functions in field theories which possess string theory duals, from the point of view of the string worldsheet. We show how the interesting ("single-trace") terms in the OPE…

The nonperturbative parton distribution and wave functions are directly related to matrix elements of light-ray (nonlocal) operators. These operators are generalizations of the standard local operators known from the operator product…