2013/07/24 by Gioia Carinci, Anna De Masi, Carinci, Gioia +5
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.1307.6385
45 pages, 2 figures
openalex publication_date 2013/07/24 · arxiv created 2013/12/01 · arxiv updated 2013/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a system of particles in the interval [0,ε-1] ∩ \mathbb Z, ε-1 a positive integer. The particles move as symmetric independent random walks (with reflections at the endpoints); simultaneously new particles are injected at site 0 at rate jε (j>0) and removed at same rate from the rightmost occupied site. The removal mechanism is therefore of topological rather than metric nature. The determination of the rightmost occupied site requires a knowledge of the entire configuration and prevents from using correlation functions techniques. We prove using stochastic inequalities that the system has a hydrodynamic limit, namely that under suitable assumptions on the initial configurations, the law of the density fields ε∑ ϕ(εx) ξε-2t(x) (ϕ a test function, ξt(x) the number of particles at site x at time t) concentrates in the limit ε→ 0 on the deterministic value ∫ ϕρt, ρt interpreted as the limit density at time t. We characterize the limit ρt as a weak solution in terms of barriers of a limit free boundary problem.