English
Related papers

Related papers: Central limit theorem for lozenge tilings with cur…

200 papers

The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in $\mathbb{R}^d$, which form a rather new, rich and flexible class of random tessellations considered in stochastic…

Probability · Mathematics 2014-12-25 Tomasz Schreiber , Christoph Thaele

We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and…

Probability · Mathematics 2015-06-12 Florent Benaych-Georges , Alice Guionnet , Camille Male

The random percolation model can be viewed as the dual of a well defined confining gauge theory; since this theory, having no Monte Carlo dynamics at all, is simple to simulate, it is possible to study the properties of the flux tube with…

High Energy Physics - Lattice · Physics 2009-04-14 Pietro Giudice , Ferdinando Gliozzi , Stefano Lottini

We study low--temperature non Gaussian thermal fluctuations of a system of classical particles around a (hypothetical) crystalline ground state. These thermal fluctuations are described by the behaviour of a system of long range interacting…

Condensed Matter · Physics 2007-05-23 Sergio Albeverio , Roman Gielerak , Helge Holden , Torbjørn Kolsrud , Mohammed Mebkhout

Finite size fluctuations are a crucial ingredient in kinetic theory of long-range interacting collisionless systems. In this Letter, we introduce a phenomenological theory which predicts an anomalous scaling close to marginal stability for…

Statistical Mechanics · Physics 2026-03-19 Yoshiyuki Y. Yamaguchi , Julien Barré

We consider Gaussian fluctuations about domain walls embedded in one- or two-dimensional spin lattices. Analytic expressions for the free energy of one domain wall are obtained. From these, the temperature dependence of experimentally…

Mesoscale and Nanoscale Physics · Physics 2014-02-04 Boris Sangiorgio , Thomas C. T. Michaels , Danilo Pescia , Alessandro Vindigni

It is expected that the statistical fluctuations of local observables in large quantum systems obey the central limit theorem, and approximate a normal distribution as their size grows. Here, we prove a version of the Berry-Esseen theorem…

We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…

Dynamical Systems · Mathematics 2020-01-08 Olli Hella , Mikko Stenlund

As in the preceding paper we aim at identifying the effective theory that describes the fluctuations of the local overlap with an equilibrium reference configuration close to a putative thermodynamic glass transition. We focus here on the…

Statistical Mechanics · Physics 2018-11-21 G. Biroli , C. Cammarota , G. Tarjus , M. Tarzia

It is becoming more and more clear that complex networks present remarkable large fluctuations. These fluctuations may manifest differently according to the given model. In this paper we re-consider hidden variable models which turn out to…

Disordered Systems and Neural Networks · Physics 2014-02-19 Massimo Ostilli

Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…

Condensed Matter · Physics 2009-10-28 Mehran Kardar

We study the unitary time evolution of the entanglement Hamiltonian of a free Fermi lattice gas in one dimension initially prepared in a domain wall configuration. To this aim, we exploit the recent development of quantum fluctuating…

Statistical Mechanics · Physics 2022-06-20 Federico Rottoli , Stefano Scopa , Pasquale Calabrese

One-dimensional interacting particle systems, 1+1 random growth models, and two-dimensional directed polymers define 2d height fields. The KPZ universality conjecture posits that an appropriately scaled height function converges to a…

Probability · Mathematics 2022-07-21 Jinho Baik

In this article we continue the study of properties of squeezing functions and geometry of bounded domains. The limit of squeezing functions of a sequence of bounded domains is studied. We give comparisons of intrinsic positive forms and…

Complex Variables · Mathematics 2013-02-25 Fusheng Deng , Qi'an Guan , Liyou Zhang

Completing the study initiated by Mounaix and Collet [J. Stat. Phys. {\bf 143}, 139-147 (2011)], we investigate the realizations of a Gaussian random field in the limit where a given (general) quadratic form of the field is large.…

Mathematical Physics · Physics 2015-09-15 Philippe Mounaix

We consider random Schr\"odinger operators with Dirichlet boundary conditions outside lattice approximations of a smooth Euclidean domain and study the behavior of its lowest-lying eigenvalues in the limit when the lattice spacing tends to…

Probability · Mathematics 2018-07-04 Marek Biskup , Ryoki Fukushima , Wolfgang Koenig

We consider Berry's random planar wave model (1977), and prove spatial functional limit theorems - in the high-energy limit - for discretized and truncated versions of the random field obtained by restricting its nodal length to rectangular…

Probability · Mathematics 2023-05-24 Massimo Notarnicola , Giovanni Peccati , Anna Vidotto

We consider the hard-edge scaling of the Mittag-Leffler ensemble confined to a fixed disk inside the droplet. Our primary emphasis is on fluctuations of rotationally-invariant additive statistics that depend on the radius and thus give rise…

Probability · Mathematics 2025-09-09 Sergey Berezin

The main result of this paper is a functional limit theorem for the sine-process. In particular, we study the limit distribution, in the space of trajectories, for the number of particles in a growing interval. The sine-process has the…

Dynamical Systems · Mathematics 2018-01-12 Alexander I. Bufetov , Andrey V. Dymov

We study the second order elliptic equations of non-divergence form in a planar domain with complicated geometry. In this case the domain winds around a fixed circle infinitely many times and converges to it when the rotating angle goes to…

Analysis of PDEs · Mathematics 2026-02-18 Luan Hoang , Akif Ibragimov