Related papers: Relation between Wick powers and excursion cluster…
Anomalous features of the proximity effect specific to diffusive normal metal / triplet superconductor (DN/TS) junctions are studied within the quasiclassical Green's function formalism. The pair amplitude $f_{N}$ as a function of energy…
We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal…
Anomalous dimensions of Wilson operators with large Lorentz spin scale logarithmically with the spin. Recent multi-loop QCD calculations of twist-two anomalous dimensions revealed the existence of interesting structure of the subleading…
In recent years, considerable interest has been drawn by the analysis of geometric functionals for the excursion sets of random eigenfunctions on the unit sphere (spherical harmonics). In this paper, we extend those results to proper…
For a non-uniform lattice in SL(2,R), we consider excursions in cusp neighborhoods of a random geodesic on the corresponding finite area hyperbolic surface or orbifold. We prove a strong law for a certain partial sum involving these…
We discuss the general operator product expansion of a non-forward unequal mass virtual compton scattering scattering amplitude. We find that the expansion now should be done in double moments with new moment variables. There are in the…
A new generalized Wick theorem for interacting fields in 2D conformal field theory is described. We briefly discuss its relation to the Borcherds identity and its derivation by an analytic method. Examples of the calculations of the…
Insight into a number of interesting questions in cosmology can be obtained from the first crossing distributions of physically motivated barriers by random walks with correlated steps. We write the first crossing distribution as a formal…
We study the convolution of functions of the form \[ f_\alpha (z) := \dfrac{\left( \frac{1 + z}{1 - z} \right)^\alpha - 1}{2 \alpha}, \] which map the open unit disk of the complex plane onto polygons of 2 edges when $\alpha\in(0,1)$. We…
We present a calculation of the spectral properties of a single charge doped at a Cu($3d$) site of the Cu-F plane in KCuF$_{3}$. The problem is treated by generating the equations of motion for the Green's function by means of subsequent…
A class of globally scale-invariant scalar-tensor theories have been proposed to be invariant under a larger class of transformations that take the form of local Weyl transformations supplemented by a restriction that the conformal factor…
Geodesic coalescence, or the tendency of geodesics to merge together, is a hallmark phenomenon observed in a variety of planar random geometries involving a random distortion of the Euclidean metric. As a result of this, the union of…
We study the Schwinger mechanism in the presence of an additional uniformly oriented, weak super Gaussian of integer order $4N+2$. Using the worldline approach, we determine the relevant critical points to compute the leading order…
We compute the correlation of analytic functions of general Gaussian fields in terms of multigraphs and Feynman diagrams on the lattice Z^d. Then, we connect its scaling limit to tensors of the correlation functionals of Fock space fields.…
The VC-dimension of a family of sets is a measure of its combinatorial complexity used in machine learning theory, computational geometry, and even model theory. Computing the VC-dimension of the $k$-fold union of geometric set systems has…
When a random field $(X_t, \ t\in {\mathbb R}^2)$ is thresholded on a given level $u$, the excursion set is given by its indicator $~1_{[u, \infty)}(X_t)$. The purpose of this work is to study functionals (as established in stochastic…
We study twist operators in higher dimensional CFT's. In particular, we express their conformal dimension in terms of the energy density for the CFT in a particular thermal ensemble. We construct an expansion of the conformal dimension in…
In this article, we shall develop and formulate two novel viewpoints and properties concerning the three-point functions at weak coupling in the SU(2) sector of the N = 4 super Yang-Mills theory. One is a double spin-chain formulation of…
This work extracts, by means of an exact analysis, the singular behaviour of the dynamical response functions -- the Fourier transforms of dynamical two-point functions -- in the vicinity of the various excitation thresholds in the massless…
In this paper we consider a random walk of a particle in $\mathbb{R}^d$. Convergence of different transformations of trajectories of random flights with Poisson switching moments has been obtained by Davydov and Konakov, as well as…