2009/11/30 by Luca Avena, L. Avena, Avena, L. +5
Mathematics · Physics and Astronomy · #35B40. #82C44 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 60H25 #Probability (math.PR) #Secondary 60F10 #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #advanced mathematical theories #math-ph #math.MP #math.PR #msc:35B40. #msc:60F10 #msc:60H25 #msc:82C44
paper · pdf · doi:10.48550/arxiv.0911.5629
24 pages, 2 figures
arxiv created 2009/11/30 · openalex publication_date 2009/11/30 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a one-dimensional shift-invariant attractive spin-flip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on vacant sites has a local drift to the left. In previous work we proved a law of large numbers for dynamic random environments satisfying a space-time mixing property called cone-mixing. If an attractive spin-flip system has a finite average coupling time at the origin for two copies starting from the all-occupied and the all-vacant configuration, respectively, then it is cone-mixing. In the present paper we prove a large deviation principle for the empirical speed of the random walk, both quenched and annealed, and exhibit some properties of the associated rate functions. Under an exponential space-time mixing condition for the spin-flip system, which is stronger than cone-mixing, the two rate functions have a unique zero, i.e., the slow-down phenomenon known to be possible in a static random environment does not survive in a fast mixing dynamic random environment. In contrast, we show that for the simple symmetric exclusion dynamics, which is not cone-mixing (and which is not a spin-flip system either), slow-down does occur.