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Related papers: Large-scale limit of interface fluctuation models

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It has recently been proposed that fluctuating ``pulled'' fronts propagating into an unstable state should not be in the standard KPZ universality class for rough interface growth. We introduce an effective field equation for this class of…

Statistical Mechanics · Physics 2009-11-07 Goutam Tripathy , Andrea Rocco , Jaume Casademunt , Wim van Saarloos

The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the…

Disordered Systems and Neural Networks · Physics 2016-08-31 Ehud Perlsman , Shlomo Havlin

We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2024-08-27 Helmut Abels , Harald Garcke , Jonas Haselböck

The height-height correlation function for a fluctuating interface between two coexisting bulk phases is derived by means of general equilibrium properties of the corresponding density-density correlation function. A wavelength-dependent…

Soft Condensed Matter · Physics 2009-11-13 Thorsten Hiester

In [arXiv:0804.3035] we studied an interacting particle system which can be also interpreted as a stochastic growth model. This model belongs to the anisotropic KPZ class in 2+1 dimensions. In this paper we present the results that are…

Statistical Mechanics · Physics 2012-10-29 Patrik L. Ferrari , Alexei Borodin

We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a…

Statistical Mechanics · Physics 2009-11-13 Hans C. Fogedby

We consider the ASEP and the stochastic six vertex model started with step initial data. After a long time, $T$, it is known that the one-point height function fluctuations for these systems are of order $T^{1/3}$. We prove the KPZ…

Probability · Mathematics 2018-05-23 Ivan Corwin , Evgeni Dimitrov

What happens when the time evolution of a fluctuating interface is interrupted with resetting to a given initial configuration after random time intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};~\alpha > 0$? For an…

Statistical Mechanics · Physics 2016-11-03 Shamik Gupta , Apoorva Nagar

We investigate the emergence of non-linear diffusivity in kinetically constrained, one-dimensional symmetric exclusion processes satisfying the gradient condition. Recent developments introduced new gradient dynamics based on the Bernstein…

Probability · Mathematics 2025-04-18 G. S. Nahum

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N x N random matrix taken from the Gaussian Unitary Ensemble (GUE).…

Mathematical Physics · Physics 2015-06-26 Yan V Fyodorov , Eugene Strahov

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

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

In this paper, we show how to use the framework of mod-Gaussian convergence in order to study the fluctuations of certain models of random graphs, of random permutations and of random integer partitions. We prove that, in these three…

Probability · Mathematics 2020-05-27 Valentin Féray , Pierre-Loïc Méliot , Ashkan Nikeghbali

We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the…

Probability · Mathematics 2019-02-05 Reda Chhaibi , Emma Hovhannisyan , Joseph Najnudel , Ashkan Nikeghbali , Brad Rodgers

We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the…

Analysis of PDEs · Mathematics 2022-01-19 Helmut Abels , Yutaka Terasawa

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

We prove global existence of weak solutions for a version of one velocity Baer-Nunziato system with dissipation describing a mixture of two non interacting viscous compressible fluids in a piecewise regular Lipschitz domain with general…

Analysis of PDEs · Mathematics 2021-05-12 Stanislav Kracmar , Young-Sam Kwon , Sarka Necasova , Antonin Novotny

A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…

Analysis of PDEs · Mathematics 2024-07-24 Nitu Lakhmara , Hari Shankar Mahato

We consider an $N$ by $N$ real or complex generalized Wigner matrix $H_N$, whose entries are independent centered random variables with uniformly bounded moments. We assume that the variance profile, $s_{ij}:=\mathbb{E} |H_{ij}|^2$,…

Probability · Mathematics 2020-08-20 Yiting Li , Yuanyuan Xu

Considering a determinantal point process on the real line, we establish a connection between the sine-kernel asymptotics for the correlation kernel and the CLT for mesoscopic linear statistics. This implies universality of mesoscopic…

Probability · Mathematics 2016-09-13 Gaultier Lambert