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Related papers: Universal Randomness

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A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn,…

Statistical Mechanics · Physics 2009-09-29 C. Vignat , A. Plastino

We establish a general version of the strong KPZ universality conjecture near the axis for random walks in a random environment (RWRE) on $\mathbb{Z}^2$. For an i.i.d. elliptic random environment, we consider the quenched large deviations…

We study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature $T$ is…

Disordered Systems and Neural Networks · Physics 2015-05-18 Pasquale Calabrese , Pierre Le Doussal , Alberto Rosso

The statistics of transmission through random 1D media are generally presumed to be universal and to depend only upon a single dimensionless parameter-the ratio of the sample length and the mean free path, s = L/l. Here, we show in…

Disordered Systems and Neural Networks · Physics 2024-07-31 Jongchul Park , Matthieu Davy , Victor A. Gopar , Azriel Z. Genack

The sequence of random probability measures $\nu_n$ that gives a path of length $n$, $\unsur{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the…

Probability · Mathematics 2008-08-29 Philippe Carmona

While originally discovered in the context of the Gaussian Unitary Ensemble, the Tracy-Widom distribution also rules the height fluctuations of growth processes. This suggests that there might be other nonequilibrium processes in which the…

Statistical Mechanics · Physics 2016-06-07 Christian B. Mendl , Herbert Spohn

We present a complete theory for the full particle statistics of the positions of bulk and extremal particles in a one-dimensional Coulomb Gas (CG) with an arbitrary potential, in the typical and large deviations regimes. Typical…

We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ universality class. For all investigated models, the RDs are given by the Tracy-Widom distribution of…

Statistical Mechanics · Physics 2011-11-10 S. G. Alves , T. J. Oliveira , S. C. Ferreira

A unified approach is proposed to describe the statistics of the short time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a…

Statistical Mechanics · Physics 2019-05-06 A. M. S. Macedo , I. R. R. Gonzales , D. S. P. Salazar , G. L. Vasconcelos

We follow the evolution with sample thickness, of intensity statistics for localized light transmitted through layered media in a crossover from one to three dimensions occasioned by transverse disorder. The probability distribution of…

Disordered Systems and Neural Networks · Physics 2013-05-29 Jongchul Park , Sheng Zhang , Azriel Z. Genack

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

Quantum Physics · Physics 2016-01-22 Jaroslav Novotný , Gernot Alber , Igor Jex

Consider the random matrix obtained from the adjacency matrix of a random d-regular graph by multiplying every entry by a random sign. The largest eigenvalue converges, after proper scaling, to the Tracy--Widom distribution.

Mathematical Physics · Physics 2016-12-20 Sasha Sodin

In spite of its simplicity, the central limit theorem captures one of the most outstanding phenomena in mathematical physics, that of universality. While this classical result is well understood it is still not very clear what happens to…

Disordered Systems and Neural Networks · Physics 2023-04-19 Ernesto Carro , Luis Benet , Isaac Pérez Castillo

We study a family of distributions that arise in critical unitary random matrix ensembles. They are expressed as Fredholm determinants and describe the limiting distribution of the largest eigenvalue when the dimension of the random…

Mathematical Physics · Physics 2011-11-16 Tom Claeys , Sheehan Olver

We prove universality of Tracy-Widom GUE fluctuations for directed polymers in $1+1$ dimensions in the intermediate disorder regime. Building on the Lindeberg replacement method of arXiv:2304.04871, we refine estimates for the measure of…

Probability · Mathematics 2025-09-29 Pranay Agarwal

The growth of the average kinetic energy of classical particles is studied for potentials that are random both in space and time. Such potentials are relevant for recent experiments in optics and in atom optics. It is found that for small…

Statistical Mechanics · Physics 2013-08-30 Yevgeny Krivolapov , Shmuel Fishman

A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…

Mathematical Physics · Physics 2017-10-05 L. Alonso , T. Gorin

A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…

Probability · Mathematics 2014-01-03 Gregory T. Clement

Signatures of universality are detected by comparing individual eigenvalue distributions and level spacings from financial covariance matrices to random matrix predictions. A chopping procedure is devised in order to produce a statistical…

Statistical Finance · Quantitative Finance 2015-05-13 Gernot Akemann , Jonit Fischmann , Pierpaolo Vivo

We establish Tracy-Widom asymptotics for the partition function of a random polymer model with gamma-distributed weights recently introduced by Sepp\"al\"ainen. We show that the partition function of this random polymer can be represented…

Probability · Mathematics 2026-01-13 Neil O'Connell , Janosch Ortmann