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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…

Probability · Mathematics 2021-06-15 Amol Aggarwal , Vadim Gorin

A description of mesoscopic fluctuations of the pairing gap in finite-sized quantum systems based on periodic orbit theory is presented. The size of the fluctuations are found to depend on quite general properties. We distinguish between…

Nuclear Theory · Physics 2011-04-11 S. Åberg , H. Olofsson , P. Leboeuf

We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions subject to projective monitoring of local charge across the measurement-induced phase transition. Our observables are…

Quantum Physics · Physics 2026-02-11 Igor Poboiko , Igor V. Gornyi , Alexander D. Mirlin

Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked…

Statistics Theory · Mathematics 2015-06-18 Damien Passemier , Matthew R. Mckay , Yang Chen

We discuss mesoscopic effects in quantum dots, nanoparticles and nuclei. In quantum dots, we focus on the statistical regime of dots whose single-electron dynamics are chaotic. Random matrix theory methods, developed to explain the…

Mesoscale and Nanoscale Physics · Physics 2009-11-11 Y. Alhassid

We consider an ensemble of fully connected networks of N oscillators coupled harmonically with random springs and show, using Random Matrix Theory considerations, that both the average phonon heat current and its variance are…

Statistical Mechanics · Physics 2015-06-15 Martin Schmidt , Tsampikos Kottos , Boris Shapiro

Using a Coulomb gas approach, we compute the generating function of the covariances of power traces for one-cut $\beta$-ensembles of random matrices in the limit of large matrix size. This formula depends only on the support of the spectral…

Mathematical Physics · Physics 2015-07-23 Fabio Deelan Cunden , Francesco Mezzadri , Pierpaolo Vivo

In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…

Machine Learning · Statistics 2024-12-10 Behrad Moniri , Hamed Hassani

We study fluctuations of linear statistics corresponding to smooth functions for certain biorthogonal ensembles. We study those biorthogonal ensembles for which the underlying biorthogonal family satisfies a finite term recurrence and…

Mathematical Physics · Physics 2013-10-09 Jonathan Breuer , Maurice Duits

Fluctuations are significant in mesoscopic systems and of particular importance in understanding quantum transport. Here, we show that fluctuations can be considered as a resource for the operations of open quantum systems as functional…

Mesoscale and Nanoscale Physics · Physics 2020-09-16 Jincheng Lu , Rongqian Wang , Chen Wang , Jian-Hua Jiang

We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…

Probability · Mathematics 2026-05-06 Solesne Bourguin , Konstantinos Spiliopoulos

We investigate the fluctuations of linear spectral statistics of a Wigner matrix $W\_N$ deformed by a deterministic diagonal perturbation $D\_N$, around a deterministic equivalent which can be expressed in terms of the free convolution…

Probability · Mathematics 2020-03-17 Sandrine Dallaporta , Maxime Fevrier

We introduce and study a class of discrete particle ensembles that naturally arise in connection with classical random matrix ensembles, log-gases and Jack polynomials. Under technical assumptions on a general analytic potential we prove…

Probability · Mathematics 2022-07-20 Evgeni Dimitrov , Alisa Knizel

Quantum coherences characterise the ability of particles to quantum mechanically interfere within some given distances. In the context of noisy many-body quantum systems these coherences can fluctuate. A simple toy model to study such…

Statistical Mechanics · Physics 2023-04-03 Ludwig Hruza , Denis Bernard

The investigation of universality questions for local eigenvalue statistics continues to be a driving force in the theory of Random Matrices. For Matrix Models [53] the method of orthogonal polynomials can be used and the asymptotics of the…

Probability · Mathematics 2016-02-25 Thomas Kriecherbauer , Kristina Schubert , Katharina Schüler , Martin Venker

We obtain uniform asymptotics for polynomials orthogonal on a fixed and varying arc of the unit circle with a positive analytic weight function. We also complete the proof of the large $s$ asymptotic expansion for the Fredholm determinant…

Functional Analysis · Mathematics 2007-05-23 I. V. Krasovsky

Covariances and variances of linear statistics of a point process can be written as integrals over the truncated two-point correlation function. When the point process consists of the eigenvalues of a random matrix ensemble, there are often…

Mathematical Physics · Physics 2022-05-04 Peter J. Forrester

We investigate the asymptotic behaviour of the second-order correlation function of the characteristic polynomial of a Hermitian Wigner matrix at the edge of the spectrum. We show that the suitably rescaled second-order correlation function…

Probability · Mathematics 2008-06-05 Holger Kösters

We study the spin-Hall conductance fluctuations in ballistic mesoscopic systems. We obtain universal expressions for the spin and charge current fluctuations, cast in terms of current-current autocorrelation functions. We show that the…

Mesoscale and Nanoscale Physics · Physics 2012-12-14 J. G. G. S. Ramos , A. L. R. Barbosa , D. Bazeia , M. S. Hussein , C. H. Lewenkopf

We present a new approach, inspired by Stein's method, to prove a central limit theorem (CLT) for linear statistics of $\beta$-ensembles in the one-cut regime. Compared with the previous proofs, our result requires less regularity on the…

Probability · Mathematics 2019-02-20 Gaultier Lambert , Michel Ledoux , Christian Webb