Related papers: Complete interpolating sequences, the discrete Muc…
This is the first in a series of articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here, we introduce spaces of…
Following a proposal of Fukaya-Ono and the exploration by B. Parker, we introduce a new transversality condition, the FOP transversality condition, for sections of orbifold vector bundles $\mathcal{E} \rightarrow \mathcal{U}$ when both…
The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this…
New sufficient conditions and necessary conditions are developed for two skew diagrams to give rise to the same skew Schur function. The sufficient conditions come from a variety of new operations related to ribbons (also known as border…
Complete Lyapunov functions for a dynamical system, given by an autonomous ordinary differential equation, are scalar-valued functions that are strictly decreasing along orbits outside the chain-recurrent set. In this paper we show that we…
Semi-parametric regression models are used in several applications which require comprehensibility without sacrificing accuracy. Typical examples are spline interpolation in geophysics, or non-linear time series problems, where the system…
In this paper we present a new compact expression of the elliptic genus of SL(2)/U(1)-supercoset theory by making use of the `spectral flow method' of the path-integral evaluation. This new expression is written in a form like a Poincare…
We introduce two Diophantine conditions on rotation numbers of interval exchange maps (i.e.m) and translation surfaces: the \emph{absolute Roth type condition} is a weakening of the notion of Roth type i.e.m., while the \emph{dual Roth…
The Sinc approximation has shown high efficiency for numerical methods in many fields. Conformal maps play an important role in the success, i.e., appropriate conformal map must be employed to elicit high performance of the Sinc…
We introduce the homogeneous and piecewise multilinear extensions and the eigenvalue problem for locally Lipschitz function pairs, in order to develop a systematic framework for relating discrete and continuous min-max problems. This also…
It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular,…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
In conformal field theory, the insertion of a defect breaks part of the global symmetry and gives rise to defect operators such as the tilts and displacements. We establish identities relating the integrated four-point functions of such…
In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function…
This work explores several aspects of interpolating sequences for $\ell^p_A$, the space of analytic functions on the unit disk with $p$-summable Maclaurin coefficients. Much of this work is communicated through a Carlesonian lens. We…
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper. The results are given in terms of $L^p$ integrability of the function and its…
We give necessary integral conditions and sufficient ones for the existence of a general concept of $\mu$-dichotomy for evolution operators defined on the half-line which includes as particular cases the well-known concepts of nonuniform…
We address the scaling limits of random curves arising from, e.g., planar lattice models, especially in rough domains. The well-known precompactness conditions of Kemppainen and Smirnov show that certain crossing probability estimates…
The modern conformal bootstrap program often employs the method of linear functionals to derive the numerical or analytical bounds on the CFT data. These functionals must have a crucial "swapping" property, allowing to swap infinite…
In the present work we discuss aspects of the 1/N expansion in the SYK model, formulated in terms of the semiclassical expansion of the bilocal field path integral. We derive cutting rules, which are applicable for all planar vertices in…