Abstract
AbstractWe study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t. This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.
Funder
Consejo Nacional de Ciencia y Tecnología
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference27 articles.
1. Carinci, G., Giardina, C., Redig, F.: Exact formulas for two interacting particles and applications in particle systems with duality, arXiv preprint arXiv:1711.11283 (2017)
2. Amir, M.: Sticky Brownian motion as the strong limit of a sequence of random walks. Stoch. Process. Appl. 39(2), 221–237 (1991)
3. Cao, J., Chleboun, P., Grosskinsky, S.: Dynamics of condensation in the totally asymmetric inclusion process. J. Stat. Phys. 155(3), 523–543 (2014)
4. Chau, Y.-X., Connaughton, C., Grosskinsky, S.: Explosive condensation in symmetric mass transport models. J. Stat. Mech. Theory Exp. 2015(11), P11031 (2015)
5. Beltrán, J., Jara, M., Landim, C.: A martingale problem for an absorbed diffusion: the nucleation phase of condensing zero range processes. Probab. Theory Relat. Fields 169(3–4), 1169–1220 (2017)
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