Related papers: The stochastic Airy operator at large temperature
Most boson emitting sources contain a core of finite dimensions surrounded by a large halo, due to long-lived resonances like $\omega,\eta,\eta',K^{0}$ etc. When the Bose-Einstein correlation (BEC) function of the core can be determined we…
We establish Poisson and compound Poisson approximations for stabilizing statistics of $\beta$-mixing point processes and give explicit rates of convergence. Our findings are based on a general estimate of the total variation distance of a…
A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…
Let $\eta_t$ be a Poisson point process of intensity $t\geq 1$ on some state space $\Y$ and $f$ be a non-negative symmetric function on $\Y^k$ for some $k\geq 1$. Applying $f$ to all $k$-tuples of distinct points of $\eta_t$ generates a…
We study the high temperature (or small inverse temperature $\beta$) expansion of the free energy of double scaled SYK model. We find that this expansion is a convergent series with a finite radius of convergence. It turns out that the…
The aim of this note is to provide a pedagogical survey of the recent works by the authors ( arXiv:1409.7548 and arXiv:1507.06013) concerning the local behavior of the eigenvalues of large complex correlated Wishart matrices at the edges…
We study spectral properties of partial differential operators modelling composite materials with highly contrasting constituents, comprised of soft spherical inclusions with random radii dispersed in a stiff matrix. Such operators have…
We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local…
For random operators it is conjectured that spectral properties of an infinite-volume operator are related to the distribution of spectral gaps of finite-volume approximations. In particular, localization and pure point spectrum in infinite…
Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's…
Chiral Random Matrix Theory has proven to describe the spectral properties of low temperature QCD very well. However, at temperatures above the chiral symmetry restoring transition it can not provide a global description. The level-spacing…
Recently we found an Anderson-type localization-delocalization transition in the QCD Dirac spectrum at high temperature. Using spectral statistics we obtained a critical exponent compatible with that of the corresponding Anderson model.…
The relaxation of the harmonical oscillator, being in contact with the thermostat whose excitations can be treated as bosons is studied. An exact temporary behavior of the inverse oscillator's temperature is obtained. In low interaction…
We prove that the largest eigenvalues of the beta ensembles of random matrix theory converge in distribution to the low-lying eigenvalues of the random Schroedinger operator -d^2/dx^2 + x + (2/beta^{1/2}) b_x' restricted to the positive…
We consider a suitable extension of the complex Airy operator, $-d^2/dx^2 + ix$, on the real line with a transmission boundary condition at the origin. We provide a rigorous definition of this operator and study its spectral properties. In…
At high temperature part of the spectrum of the quark Dirac operator is known to consist of localized states. This comes about because around the crossover temperature to the quark-gluon plasma localized states start to appear at the low…
In this paper we prove the convergence of the eigenvalues of a random matrix that approximates a random Schr\"{o}dinger operator. Originally, such random operator arises from a stochastic heat equation. The proof uses a detailed topological…
Bessel processes associated with the root systems $A_{N-1}$ and $B_N$ describe interacting particle systems with $N$ particles on $\mathbb R$; they form dynamic versions of the classical $\beta$-Hermite and Laguerre ensembles. In this paper…
This is the second paper in a series studying the global asymptotics of discrete $N$-particle systems with inverse temperature parameter $\theta$ in the high temperature regime. In the first paper, we established necessary and sufficient…
We investigate the behavior of the spectrum of the continuous Anderson Hamiltonian $\mathcal{H}_L$, with white noise potential, on a segment whose size $L$ is sent to infinity. We zoom around energy levels $E$ either of order $1$ (Bulk…