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Related papers: Brownian structure in the KPZ fixed point

200 papers

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

We study the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) interfaces growing inward from ring-shaped initial conditions, experimentally and numerically, using growth of a turbulent state in liquid-crystal electroconvection and an…

Statistical Mechanics · Physics 2017-08-14 Yohsuke T. Fukai , Kazumasa A. Takeuchi

The Kardar-Parisi-Zhang (KPZ) equation on the real line is well-known to admit Brownian motion with a linear drift as a stationary distribution (modulo additive constants). We show that these solutions are attractive, a result known as a…

Probability · Mathematics 2022-11-15 Christopher Janjigian , Firas Rassoul-Agha , Timo Seppäläinen

We consider an infinite system of Brownian motions which interact through a given Brownian motion being reflected from its left neighbor. Earlier we studied this system for deterministic periodic initial configurations. In this contribution…

Mathematical Physics · Physics 2017-02-14 Patrik L. Ferrari , Herbert Spohn , Thomas Weiss

This paper is a step in the direction of understanding the behavior of non-intersecting Brownian motions on the real line, when the number of particles becomes large. Consider 2k non-intersecting Brownian motions, all starting at the…

Probability · Mathematics 2007-05-23 Mark Adler , Pierre van Moerbeke

We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equation in one and two dimensions in order to study the scaling properties of the interface at the depinning transition. Specifically, the $\alpha$, $\beta$,…

We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate…

Statistical Mechanics · Physics 2014-01-14 Silvia N. Santalla , Javier Rodriguez-Laguna , Rodolfo Cuerno

Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal…

Statistical Mechanics · Physics 2009-11-07 M. Myllys , J. Maunuksela , M. Alava , T. Ala-Nissila , J. Merikoski , J. Timonen

We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved…

Statistical Mechanics · Physics 2013-05-15 Sidiney G. Alves , Tiago J. Oliveira , Silvio C. Ferreira

A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit non-equilibrium phase transitions, which…

Condensed Matter · Physics 2015-06-24 Miguel A. Munoz , F. de los Santos , A. Achahbar

We explore the critical dynamics of driven interfaces propagating through a two dimensional disordered medium with long range spatial correlations, modeled using fractional Brownian motion. Departing from conventional models with…

Statistical Mechanics · Physics 2025-10-02 Neda Valizadeh , Morteza Nattagh Najafi

An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary right-finite initial condition. The method is by solving…

Probability · Mathematics 2021-11-25 Konstantin Matetski , Jeremy Quastel , Daniel Remenik

We provide a framework for proving convergence to the directed landscape, the central object in the Kardar-Parisi-Zhang universality class. For last passage models, we show that compact convergence to the Airy line ensemble implies…

Probability · Mathematics 2022-10-13 Duncan Dauvergne , Bálint Virág

The Kardar-Parisi-Zhang (KPZ) equation for surface growth has been analyzed for over three decades. Some experiments indicated the power law for the interface width, $w(t)\sim t^\beta$, remains the same as in growth on planar surfaces.…

We revisit the anchored Toom interface and use KPZ scaling theory to argue that the interface fluctuations are governed by the Airy_1 process with the role of space and time interchanged. There is no free parameter. The predictions are…

Mathematical Physics · Physics 2015-06-19 G. T. Barkema , P. L. Ferrari , J. L. Lebowitz , H. Spohn

We discuss chains of interacting Brownian motions. Their time reversal invariance is broken because of asymmetry in the interaction strength between left and right neighbor. In the limit of a very steep and short range potential one arrives…

Mathematical Physics · Physics 2014-11-13 Tomohiro Sasamoto , Herbert Spohn

We study the solution of the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line, equivalently the free energy of the continuum directed polymer in a half space with a…

Statistical Mechanics · Physics 2021-08-05 Guillaume Barraquand , Alexandre Krajenbrink , Pierre Le Doussal

We present an exact solution for the probability density function $P(\tau=t_{\min}-t_{\max}|T)$ of the time-difference between the minimum and the maximum of a one-dimensional Brownian motion of duration $T$. We then generalise our results…

Statistical Mechanics · Physics 2020-04-20 Francesco Mori , Satya N. Majumdar , Gregory Schehr

We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the…

Materials Science · Physics 2009-02-01 A. Kolakowska , M. A. Novotny , P. S. Verma

This Letter reports on how the interfaces in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) class undergo, in the course of time, a transition from the flat, growing regime to the stationary one. Simulations of the polynuclear growth model…

Statistical Mechanics · Physics 2013-06-03 Kazumasa A. Takeuchi