相关论文: Mathematics of random growing interfaces

We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…

The restricted solid-on-solid (RSOS) model is a model of continuous-time surface growth characterized by the constraint that adjacent height differences are bounded by a fixed constant. Though the model is conjectured to belong to the KPZ…

We show that the probability, P_0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P_0(l) \sim…

We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form…

Thermal fluctuations cause the local normal vectors of fluid interfaces to deviate from the vertical direction defined by the flat mean interface position. This leads to a nonzero mean value of the corresponding polar tilt angle which…

We study a random resistors network model on a euclidean geometry $\bt{Z}^d$. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per…

The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near…

We study the persistence properties in a simple model of two coupled interfaces characterized by heights h_1 and h_2 respectively, each growing over a d-dimensional substrate. The first interface evolves independently of the second and can…

We extend the weak universality of KPZ in [Hairer-Quastel] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on correlations of trigonometric functions of…

We investigate the interface dynamic in Laplacian growth model, using the conformal mapping technique. Starting from the governing equation for the conformal map, obtained by B.Shraiman and D.Bensimon, we derive different possible forms of…

We introduce a variation of the classic ballistic deposition model in which vertically falling blocks can only stick to the top or the upper right corner of growing columns. We establish that fluctuations of the height function at points…

A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common…

The raise and peel model of a one-dimensional fluctuating interface (model A) is extended by considering one source (model B) or two sources (model C) at the boundaries. The Hamiltonians describing the three processes have, in the…

We propose a simple, exactly solvable, model of interface growth in a random medium that is a variant of the zero-temperature random-field Ising model on the Cayley tree. This model is shown to have a phase diagram (critical depinning field…

There is mounting evidence indicating that relaxation dynamics in liquids approaching their glass transition not only becomes increasingly cooperative (1,2) but the relaxing regions also become more compact in shape(3-7). While the surface…

A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…

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…

We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affect the state of its neighbours. We give…

Imbibition phenomena have been widely used experimentally and theoretically to study the kinetic roughening of interfaces. We critically discuss the existing experiments and some associated theoretical approaches on the scaling properties…

The dimer model on a planar bipartite graph can be viewed as a random surface measure. We study these fluctuations for a dimer model on the square grid with two different classes of weights and provide a condition for their equivalence. In…