Related papers: Chordal Loewner families and univalent Cauchy tran…

We consider probability measures arising from the Cauchy summation identity for the LLT (Lascoux--Leclerc--Thibon) symmetric polynomials of rank $n \geq 1$. We study the asymptotic behaviour of these measures as one of the two sets of…

We present necessary and sufficient conditions on systems of random variables for them to possess a lacunary subsystem equivalent in distribution to the Rademacher system on the segment [0,1]. In particular, every uniformly bounded…

We consider multipoint Pad\'e approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium…

We introduce a class of central symmetric infinitely divisible probability measures on compact Lie groups by lifting the characteristic exponent from the real line via the Casimir operator. The class includes Gauss, Laplace and stable-type…

We construct generalized regular representations of the wreath product of a compact group with the infinite symmetric group. The characters of these representations are determined by probability measures on families of partitions called the…

We prove that any disjoint union of finitely many simple curves in the upper half-plane can be generated in a unique way by the chordal multiple-slit Loewner equation with constant weights.

Let $G$ be an infinite residually finite group. We show that for every minimal equicontinuous Cantor system $(Z,G)$ with a free orbit, and for every minimal extension $(Y,G)$ of $(Z,G)$, there exist a minimal almost 1-1 extension $(X,G)$ of…

This paper studies estimation of and inference on a distribution function $F$ that is concave on the nonnegative half line and admits a density function $f$ with potentially unbounded support. When $F$ is strictly concave, we show that the…

The problem of measuring an unbounded system attribute near a singularity has been discussed. Lenses have been introduced as formal objects to study increasingly precise measurements around the singularity and a specific family of lenses…

Hadwiger's transversal theorem gives necessary and sufficient conditions for a family of convex sets in the plane to have a line transversal. A higher dimensional version was obtained by Goodman, Pollack and Wenger, and recently a colorful…

We construct with full rigorous mathematical proof a family of approximate solutions to the Cauchy problem for the standard system of two fluid flows with energy equations and we pass to the limit by weak compactness to obtain Radon…

Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions.…

The three cardinal, statistically consistent, families of non-parametric estimators to the power spectral density of a time series are lag-window, multitaper and Welch estimators. However, when estimating power spectral densities from a…

In this note we discuss some problems related to conformal slit-mappings. On the one hand, classical Loewner theory leads us to questions concerning the embedding of univalent functions into slit-like Loewner chains. On the other hand, a…

Consider the family of automorphic representations on a unitary group with cohomological factor $\pi_0$ at infinity and given split level. We compute statistics of this family as the level goes to infinity. For unramified unitary groups and…

We give an equivalence-singularity criterion for infinite products of Cauchy measures under simultaneous shifts of the location and scale parameters. Our result is an extension of Lie and Sullivan's result giving an equivalence-singularity…

We prove a central limit theorem (CLT) for the number of joint orbits of random tuples of commuting permutations. In the uniform sampling case this generalizes the classic CLT of Goncharov for the number of cycles of a single random…

We show the convergence of the characteristic polynomial for random permutation matrices sampled from the generalized Ewens distribution. Under this distribution, the measure of a given permutation depends only on its cycle structure,…

We define genus zero open Gromov-Witten invariants with boundary and interior constraints for a Lagrangian submanifold of arbitrary even dimension. The definition relies on constructing a canonical family of bounding cochains that satisfy…

In this article we investigate high-dimensional banded sample covariance matrices under the regime that the sample size $n$, the dimension $p$ and the bandwidth $d$ tend simultaneously to infinity such that $$n/p\to 0 \ \ \text{and} \ \…