Related papers: The Cusp-Airy Process
We consider a large class of deformations of continuous and discrete biorthogonal ensembles and investigate their behavior in the limit of a large number of particles. We provide sufficient conditions to ensure that if a biorthogonal…
We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk…
How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a…
We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this distribution. In the latter case we observe a new…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…
This paper is a step in the direction of understanding the behavior of non-intersecting Brownian motions on the real line, when the number of particles becomes large. Consider 2k non-intersecting Brownian motions, all starting at the…
The parabolic Airy process is the Airy$_2$ process minus a parabola, initially defined by its finite-dimensional distributions, which are given by a Fredholm determinant formula with the extended Airy kernel. This process is also the…
We prove that matrix Fredholm determinants related to multi-time processes can be expressed in terms of determinants of integrable kernels \`a la Its-Izergin-Korepin-Slavnov (IIKS) and hence related to suitable Riemann-Hilbert problems,…
We theoretically study topological laser operation in a bosonic Harper-Hofstadter model featuring a saturable optical gain. Crucial consequences of the chirality of the lasing edge modes are highlighted, such as a sharp dependence of the…
We consider the convex hull of the perturbed point process comprised of $n$ i.i.d. points, each distributed as the sum of a uniform point on the unit sphere $\S^{d-1}$ and a uniform point in the $d$-dimensional ball centered at the origin…
Airy and Pearcey-like kernels and generalizations arising in random matrix theory are expressed as double integrals of ratios of exponentials, possibly multiplied with a rational function. In this work it is shown that such kernels are…
In these lecture we explain why limiting distribution function, like the Tracy-Widom distribution, or limit processes, like the Airy_2 process, arise both in random matrices and interacting particle systems. The link is through a common…
This paper deals with the intersection point process of a stationary and isotropic Poisson hyperplane process in $\mathbb{R}^d$ of intensity $t>0$, where only hyperplanes that intersect a centred ball of radius $R>0$ are considered. Taking…
We find the probability of two gaps of the form $(sc,sb)\cup (sa,+\infty)$, $c<b<a<0$, for large $s>0$, in the edge scaling limit of the Gaussian Unitary Ensemble of random matrices, including the multiplicative constant in the asymptotics.
We start by studying a peeling process on finite random planar maps with faces of arbitrary degrees determined by a general weight sequence, which satisfies an admissibility criterion. The corresponding perimeter process is identified as a…
By applying an idea of Borodin and Olshanski [J. Algebra 313 (2007), 40-60], we study various scaling limits of determinantal point processes with trace class projection kernels given by spectral projections of selfadjoint Sturm-Liouville…
A wave near an isolated turning point is typically assumed to have an Airy function profile with respect to the separation distance. This description is incomplete, however, and is insufficient to describe the behavior of more realistic…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
We describe a method to evaluate integrals that arise in the asymptotic analysis when two saddle points may be close together. These integrals, which appear in problems from optics, acoustics or quantum mechanics as well as in a wide class…
This paper establishes a universality result for scaling limits of uniformly random lozenge tilings of large domains. We prove that whenever a boundary of the domain has three adjacent straight segments inclined under 120 degrees to each…