Related papers: SLE_k: correlation functions in the coefficient pr…
A model-independent method for the analysis of the two-particle short-range correlations is presented, that can be utilized to describe e.g. Bose-Einstein (HBT), dynamical (ridge) or other correlation functions, that have a nearly L\'evy or…
We show that, under mild assumptions on the limiting curve, a sequence of simple chordal planar curves converges uniformly whenever certain Loewner driving functions converge. We extend this result to random curves. The random version…
We consider multiple chordal Schramm-Loewner evolution (SLE) with $\kappa\in (0,4]$. Under common-time parameterization, we show that the transition density of the driving function of multiple chordal SLEs can be given by the transition…
We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory. For this purpose,…
We analyze the coefficients of partition functions of Vafa-Witten theory for the complex projective plane $\mathbb{CP}^2$. We experimentally study the growth of the coefficients for gauge group $SU(2)$ and $SU(3)$, which are examples of…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…
In this paper new classes of $L_2$-orthogonal functions are constructed as iterated $L_2$-orthogonal systems. In order to do this we use the theory of the Riemann's zeta-function as well as our theory of Jacob's ladders. The main result is…
We apply the bootstrap technique to find the moments of certain multi-trace and multi-matrix random matrix models suggested by noncommutative geometry. Using bootstrapping we are able to find the relationships between the coupling constant…
The Shcramm-Loewner evolution (SLE) is a correlated exploration process, in which for the chordal set up, the tip of the trace evolves in a self-avoiding manner towards the infinity. The resulting curves are named SLE$_{\kappa}$,…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
We relate the formulas giving Brownian (and other) intersection exponents to the absolute continuity relations between Bessel process of different dimensions, via the two-parameter family of Schramm-Loewner Evolution processes…
In this note, we study two-point correlation functions of modular Hamiltonians. We show that in general quantum systems, these correlators obey properties similar to those of von Neumann entropy and capacity of entanglement, both of which…
Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever…
Like categories, small 2-categories have well-understood classifying spaces. In this paper, we deal with homotopy types represented by 2-diagrams of 2-categories. Our results extend to homotopy colimits of 2-functors lower categorical…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
We consider multi-variable sigma function of a genus $g$ hyperelliptic curve as a function of two group of variables -jacobian variables and parameters of the curve. In the theta-functional representation of sigma-function, the second group…
The paper addresses linear hyperbolic systems in one space dimension with random field coefficients. In many applications, a low degree of regularity of the paths of the coefficients is required, which is not covered by classical stochastic…
In part 1 (Chapter 2) we present the basic notions of Loewner theory. Here we use a modern form which was developed by F. Bracci, M. Contreras, S. D\'iaz-Madrigal et al. and which can be applied to certain higher dimensional complex…
We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be…
Ordinary SLE$_{k}$ is defined using a Wiener noise and is related to CFT's which have null vector at level two of conformal tower. In this paper we introduce stochastic variables which are made up of jumps and extend the ordinary SLE to…