Density fluctuations for exclusion processes with long jumps

• 成果类型: Article
• 署名作者: Goncalves, Patricia; Jara, Milton
• 署名单位: Universidade de Lisboa
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0758-0
• 发表日期: 2018
• 页码: 311-362
• 关键词: interacting particle-systems; asymmetric simple exclusion; conservative spin systems; central-limit-theorem; equilibrium fluctuations; additive-functionals; harmonic-oscillators; tagged particle; spectral gap; superdiffusion

摘要

We show that the stationary density fluctuations of exclusion processes with long jumps, whose rates are of the form where depends on the sign of , are given by a fractional Ornstein-Uhlenbeck process for . When we show that the density fluctuations are tight, in a suitable topology, and that any limit point is an energy solution of the fractional Burgers equation, previously introduced in Gubinelli and Jara (Stoch Partial Differ Equ Anal Comput 1(2):325-350, 2013) in the finite volume setting.