Related papers: Conformal restriction: the radial case

We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved.…

We give a recursive method to compute the classical conformal blocks in Liouville field theory. The values of the expansion coefficients are given by an algebraic scheme which works to all orders. The algebraic expression of the intervening…

It is shown that the radial Schroedinger equation for a power law potential and a particular angular momentum may be transformed using a change of variable into another Schroedinger equation for a different power law potential and a…

The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…

Inspired by Gaiotto's conformal limit construction for Higgs bundles we define and study a conformal limit construction for Nakajima quiver varieties. We prove that the conformal limit is indeed a limit of a one parameter family of points…

We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of…

We study integrability and continuity properties of random series of Hermite functions. We get optimal results which are analogues to classical results concerning Fourier series, like the Paley-Zygmund or the Salem-Zygmund theorems. We also…

Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty…

This paper addresses the so-called conformal capacities in $\mathbb R^n$, $n\ge 3$, through comparing three existing definitions (due to Betsakos, Colesanti-Cuoghi, Anderson-Vamananmurthy-Fuglede respectively) and studying their associated…

We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…

We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle given in terms of the exponential of Gaussian Free Field. We conjecture that our curves are locally…

We establish variational estimates related to the problem of restricting the Fourier transform of a three-dimensional function to the two-dimensional Euclidean sphere. At the same time, we give a short survey of the recent field of maximal…

We stduy $L^p-L^r$ restriction estimates for algebraic varieties $V$ in the case when restriction operators act on radial functions in the finite field setting. We show that if the varieties $V$ lie in odd dimensional vector spaces over…

For a conformal manifold, we describe a new relation between the ambient obstruction tensor of Fefferman and Graham and the holonomy of the normal conformal Cartan connection. This relation allows us to prove several results on the…

We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we…

In this note, we give a probabilistic interpretation of the Central Limit Theorem used for approximating isotropic Gaussians in [1].

We propose a fairly simple and natural extension of Stollmann's lemma to correlated random variables. This extension allows (just as the original Stollmann's lemma does) to obtain Wegner-type estimates even in some problems of spectral…

Conformal prediction offers a distribution-free framework for constructing prediction sets with coverage guarantees. In practice, multiple valid conformal prediction sets may be available, arising from different models or methodologies.…

In this paper, we determine the partial positivity(resp., negativity) of the curvature of all irreducible Riemannian symmetric spaces. From the classifications of abstract root systems and maximal subsystems, we can give the calculations…

The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a…