2004/07/02 by Éric Brunet-Gouet, Eric Brunet, Bernard Derrida
Computer Science · Mathematics · Physics and Astronomy · #Constant (computer programming) #Diffusion #Exact solutions in general relativity #Fick's laws of diffusion #Limit (mathematics) #Materials science #Mathematical analysis #Mathematics #Noise (video) #Nonlinear Dynamics and Pattern Formation #Physics #Position (finance) #Quantum mechanics #Range (aeronautics) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Traveling wave #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.70.016106
published as Phys. Rev. E 70, 016106 (2004) · 5 pages
openalex publication_date 2004/07/02 · arxiv created 2004/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We calculate exactly the velocity and diffusion constant of a microscopic stochastic model of N evolving particles which can be described by a noisy traveling-wave equation with a noise of order N(-1/2). Our model can be viewed as the infinite range limit of a directed polymer in random medium with N sites in the transverse direction. Despite some peculiarities of the traveling-wave equations in the absence of noise, our exact solution allows us to test the validity of a simple cutoff approximation and to show that, in the weak noise limit, the position of the front can be completely described by the effect of the noise on the first particle.