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The probabilities $P_\pm(t_0,t)$ that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval $(t_0, t)$ are shown numerically to decay as $P_\pm \sim (t_0/t)^{\theta_\pm}$ with $\theta_+ = 1.18…

Statistical Mechanics · Physics 2009-10-31 Harald Kallabis , Joachim Krug

We introduce a geometric scaling relation that characterizes the local scale behavior of correlations using the informational distance $d_E = K_0/\sqrt{I}$, where $I$ is the mutual information. We define a geometric conversion factor, $G…

Statistical Mechanics · Physics 2025-12-02 Beau Leighton-Trudel

In this paper, we study the probability distribution of the observable $s = (1/N)\sum_{i=N-N'+1}^N x_i$, with $1 \leq N' \leq N$ and $x_1<x_2<\cdots< x_N$ representing the ordered positions of $N$ particles in a $1d$ one-component plasma,…

Statistical Mechanics · Physics 2021-10-12 Ana Flack , Satya N. Majumdar , Gregory Schehr

Scale-invariant fluctuations of growing interfaces are studied for circular clusters of an off-lattice variant of the Eden model, which belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. Statistical properties of…

Statistical Mechanics · Physics 2012-05-15 Kazumasa A. Takeuchi

We consider an infinite interface in $d>2$ dimensions, governed by the Kardar-Parisi-Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability…

Statistical Mechanics · Physics 2018-05-02 Baruch Meerson , Pavel V. Sasorov , Arkady Vilenkin

We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y(t)= h(t)-< h(t)>, which is depicted as being subordinated to a standard…

Adaptation and Self-Organizing Systems · Physics 2009-11-10 R. Failla , P. Grigolini , M. Ignaccolo , A. Schwettmann

This paper studies the trade-off between the degree of decentralization and the performance of a distributed controller in a linear-quadratic control setting. We study a system of interconnected agents over a graph and a distributed…

Optimization and Control · Mathematics 2026-05-11 Sungho Shin , Yiheng Lin , Guannan Qu , Adam Wierman , Mihai Anitescu

The coupled entropy, $H_\kappa,$ is proven to uniquely satisfy the requirement that a generalized entropy be a measure of the uncertainty at the scale, $\sigma,$ for a class of non-exponential distributions. The coupled stretched…

Statistical Mechanics · Physics 2026-01-14 Kenric P. Nelson

In this article we study the scaling limit of the interface model on $\mathbb{Z}^d$ where the Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any dimension the scaling limit is given by the Gaussian free…

Probability · Mathematics 2020-05-05 Alessandra Cipriani , Biltu Dan , Rajat Subhra Hazra

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling…

Disordered Systems and Neural Networks · Physics 2018-05-24 Alexander K. Hartmann , Pierre Le Doussal , Satya N. Majumdar , Alberto Rosso , Gregory Schehr

We study the interface representation of the contact process (CP) at its directed-percolation critical point, where the scaling properties of the interface can be related to those of the original particle model. Interestingly, such a…

Statistical Mechanics · Physics 2024-09-30 B. G. Barreales , J. J. Meléndez , R. Cuerno , J. J. Ruiz-Lorenzo

In this letter, some applications of wireless communication systems over $\alpha-\eta-\kappa-\mu$ fading channels are analysed. More specifically, the effective rate and the average of both the detection probability and area under the…

Information Theory · Computer Science 2019-09-17 Hussien Al-Hmood , H. S. Al-Raweshidy

We determine the exact short-time distribution $-\ln \mathcal{P}_{\text{f}}\left(H,t\right)= S_{\text{f}} \left(H\right)/\sqrt{t}$ of the one-point height $H=h(x=0,t)$ of an evolving 1+1 Kardar-Parisi-Zhang (KPZ) interface for flat initial…

Statistical Mechanics · Physics 2018-05-16 Naftali R. Smith , Baruch Meerson

We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if kappa^{<kappa}=kappa then there is such a space of height kappa^+ with…

Logic · Mathematics 2007-05-23 Istvan Juhász , Saharon Shelah , Lajos Soukup , Zoltan Szentmiklóssy

This work considers the behavior of the height distributions of the equipotential lines in a region confined by two interfaces: a cathode with an irregular interface and a distant flat anode. Both boundaries, which are maintained at…

Computational Physics · Physics 2014-10-08 C. P. de Castro , T. A. de Assis , C. M. C. de Castilho , R. F. S. Andrade

We consider the $1d$ one-component plasma (OCP) in thermal equilibrium, consisting of $N$ equally charged particles on a line, with pairwise Coulomb repulsion and confined by an external harmonic potential. We study two observables: (i) the…

Statistical Mechanics · Physics 2022-06-10 Ana Flack , Satya N. Majumdar , Gregory Schehr

The generally accepted representation of $\kappa$-distributions in space plasma physics allows for two different alternatives, namely assuming either the temperature or the thermal velocity to be $\kappa$-independent. The present paper aims…

Solar and Stellar Astrophysics · Physics 2016-04-13 M. Lazar , H. Fichtner , P. H. Yoon

Covariance matrix of heights measured relative to the average height of a growing self-affine surface in the steady state are investigated in the framework of random matrix theory. We show that the spectral density of the covariance matrix…

Statistical Mechanics · Physics 2015-06-11 Hyun-Joo Kim , Doil Jung

We consider a model of first passage percolation (FPP) where the nearest-neighbor edges of the standard two-dimensional Euclidean lattice are equipped with random variables. These variables are i.i.d.\, nonnegative, continuous, and have a…

Probability · Mathematics 2021-05-06 Ujan Gangopadhyay

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to…

Statistical Mechanics · Physics 2009-11-13 T. W. Burkhardt , G. Gyorgyi , N. R. Moloney , Z. Racz