Related papers: Wiener densities for the Airy line ensemble

The following anticoncentration property is proved. The probability that the $k$-order statistic of an arbitrarily correlated jointly Gaussian random vector $X$ with unit variance components lies within an interval of length $\varepsilon$…

Using a factorization theorem due to Pasynkov we provide a short proof of the existence and density of parametric Bing and Krasinkiewicz maps. In particular, the following corollary is established: Let $f\colon X\to Y$ be a surjective map…

We generalize results of Alladi, Dawsey, and Sweeting and Woo for Chebotarev densities to general densities of sets of primes. We show that if $K$ is a number field and $S$ is any set of prime ideals with natural density $\delta(S)$ within…

Suppose V is a surface over a number field k that admits two elliptic fibrations. We show that for each integer d there exists an explicitly computable closed subset Z of V, not equal to V, such that for each field extension K of k of…

We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…

Given a finite set of points $S\subset\mathbb{R}^d$, a $k$-set of $S$ is a subset $A \subset S$ of size $k$ which can be strictly separated from $S \setminus A $ by a hyperplane. Similarly, a $k$-facet of a point set $S$ in general position…

We establish an unexpected phenomenon of strong regularization along normal convergence on Wiener chaoses. For every sequence of chaotic random variables, convergence in law to the Gaussian distribution is upgraded to superconvergence: the…

The Airy$_\beta$ line ensemble is an infinite sequence of random curves. It is a natural extension of the Tracy-Widom$_\beta$ distributions, and is expected to be the universal edge scaling limit of a range of models in random matrix theory…

The filtering equations associated to a partially observed jump diffusion model $(Z_t)_{t\in [0,T]}=(X_t,Y_t)_{t\in [0,T]}$, driven by Wiener processes and Poisson martingale measures are considered. Building on results from two preceding…

In (J. Stat. Phys. 132, 275-290, 2008) Borodin and P\'ech\'e introduced a generalization of the extended Airy kernel based on two infinite sets of parameters. For an arbitrary choice of parameters we construct determinantal point processes…

Let K be any compact set in the complex plane that has a connected complement, let A(K) be the uniforn algebra of all continuous complex functions on K that are holomorphic on the interior of K, let bK be the topological boundary of K, let…

We consider the Brown measure of $a+\mathfrak{c}$, where $a$ lies in a commutative tracial von Neumann algebra $\mathcal{B}$ and $\mathfrak{c}$ is a $\mathcal{B}$-valued circular element. Under certain regularity conditions on $a$ and the…

We classify invariant probability measures for non-elementary groups of automorphisms, on any compact K\"ahler surface X, under the assumption that the group contains a so-called "parabolic automorphism". We also prove that except in…

We consider Dyson Brownian motion for classical values of $\beta$ with deterministic initial data $V$. We prove that the local eigenvalue statistics coincide with the GOE/GUE in the fixed energy sense after time $t \gtrsim 1/N$ if the…

We show that a relatively ergodic extension of measure-preserving dynamical systems has relative discrete spectrum if and only if it can be represented as a skew-product by a bundle of compact homogeneous spaces. Our result holds without…

We prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary in an unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our…

The aim of this article is to prove Zariski density of crystalline representations in the rigid analytic space associated to the universal deformation ring of a d-dimensional mod p representation of Gal(\bar{K}/K) for any d and for any…

In a recent work, we proved that under diffusive scaling, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2 converges in distribution to the Brownian web. In…

In this article, we propose a way to consider processes indexed by a collection $\mathcal{A}$ of subsets of a general set $\mathcal{T}$. A large class of vector spaces, manifolds and continuous $\mathbb{R}$-trees are particular cases.…

Let $T$ be an ergodic measure-preserving transformation on a non-atomic probability space $(X,\Sigma,\mu)$. We prove uniform extensions of the Wiener-Wintner theorem in two settings: For averages involving weights coming from Hardy field…