English
Related papers

Related papers: Exact Maximal Height Distribution of Fluctuating I…

200 papers

The free-energy distribution function of an elastic string in a quenched random potential, P(F), is investigated with the help of the optimal-fluctuation approach. The form of the far-right tail of P(F) is found by constructing the exact…

Disordered Systems and Neural Networks · Physics 2015-05-13 I. V. Kolokolov , S. E. Korshunov

We study the complete probability distribution $\mathcal{P}\left(\bar{H},t\right)$ of the time-averaged height $\bar{H}=(1/t)\int_0^t h(x=0,t')\,dt'$ at point $x=0$ of an evolving 1+1 dimensional Kardar-Parisi-Zhang (KPZ) interface…

Statistical Mechanics · Physics 2019-07-09 Naftali R. Smith , Baruch Meerson , Arkady Vilenkin

We numerically study the distribution function of the conductance (transmission) in the one-dimensional tight-binding Anderson and periodic-on-average superlattice models in the region of fluctuation states where single parameter scaling is…

Disordered Systems and Neural Networks · Physics 2009-11-10 L. I. Deych , M. V. Erementchouk , A. A. Lisyansky , Alexey Yamilov , Hui Cao

We study an anomalous behavior of the height fluctuation width in the crossover from random to coherent growths of surface for a stochastic model. In the model, random numbers are assigned on perimeter sites of surface, representing pinning…

Statistical Mechanics · Physics 2009-10-28 K. Park , B. Kahng

We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one--dimensional integer lattice and grows in discrete time: (1) the height above the site $x$…

Probability · Mathematics 2007-05-23 Janko Gravner , Craig A. Tracy , Harold Widom

For stationary interface growth, governed by the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik-Rains distribution. Recently Chhita et al. [1]…

Statistical Mechanics · Physics 2017-11-22 Baruch Meerson , Johannes Schmidt

We present a scheme to accurately calculate the persistence probabilities on sequences of $n$ heights above a level $h$ from the measured $n+2$ points of the height-height correlation function of a fluctuating interface. The calculated…

Statistical Mechanics · Physics 2010-03-10 J. M. J. van Leeuwen , V. W. A. de Villeneuve , H. N. W. Lekkerkerker

We numerically study the distribution function of the conductivity (transmission) in the one-dimensional tight-binding Anderson model in the region of fluctuation states. We show that while single parameter scaling in this region is not…

Disordered Systems and Neural Networks · Physics 2009-11-07 L. I. Deych , M. V. Erementchouk , A. A. Lisyansky

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers of mass remain…

Computational Physics · Physics 2020-12-30 Clemens Moritz , Marcello Sega , Max Innerbichler , Phillip L. Geissler , Christoph Dellago

We consider an effective interface model on a hard wall in (1+1) dimensions, with conservation of the area between the interface and the wall. We prove that the equilibrium fluctuations of the height variable converge in law to the solution…

Probability · Mathematics 2007-11-06 Lorenzo Zambotti

We study numerically the correlations and the distribution of intervals between successive zeros in the fluctuating geometry of stochastic interfaces, described by the Edwards-Wilkinson equation. For equilibrium states we find that the…

Statistical Mechanics · Physics 2016-06-22 Arturo L. Zamorategui , Vivien Lecomte , Alejandro B. Kolton

We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a…

Probability · Mathematics 2025-12-22 Yu Gu , Ran Tao

We study a system of $N$ non-intersecting $(1+1)$-dimensional fluctuating elastic interfaces (`vicious bridges') at thermal equilibrium, each subject to periodic boundary condition in the longitudinal direction and in presence of a…

Statistical Mechanics · Physics 2015-05-13 Céline Nadal , Satya N. Majumdar

We report exact predictions for universal scaling exponents and scaling functions associated with the distribution of the maximum collective avalanche propagation velocities $v_m$ in the mean field theory of the interface depinning…

Disordered Systems and Neural Networks · Physics 2015-06-15 Michael LeBlanc , Luiza Angheluta , Karin Dahmen , Nigel Goldenfeld

We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear…

Statistical Mechanics · Physics 2009-10-31 Z. Toroczkai , G. Korniss , S. Das Sarma , R. K. P. Zia

An unbounded one-dimensional solid-on-solid model with integer heights is studied. Unbounded here means that there is no a priori restrictions on the discret e gradient of the interface. The interaction Hamiltonian of the interface is given…

Probability · Mathematics 2010-10-11 Gustavo Posta

Numerical and analytical results are presented for the maximal relative height distribution of stationary periodic Gaussian signals (one dimensional interfaces) displaying a 1/f^alpha power spectrum. For 0<alpha<1 (regime of decaying…

Statistical Mechanics · Physics 2013-05-29 G. Gyorgyi , N. R. Moloney , K. Ozogany , Z. Racz

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 study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1…

Statistical Mechanics · Physics 2015-05-18 Joachim Rambeau , Gregory Schehr

We study one-dimensional fluctuating interfaces of length $L$ where the interface stochastically resets to a fixed initial profile at a constant rate $r$. For finite $r$ in the limit $L \to \infty$, the system settles into a nonequilibrium…

Statistical Mechanics · Physics 2014-06-04 Shamik Gupta , Satya N. Majumdar , Gregory Schehr