 Gibbs-non-Gibbs dynamical transitions for mean-field interacting Brownian motionsF. den Hollander, F. Redig and W. van Zuijlen Stochastic Processes and their Applications, 2015, vol. 125, issue 1, 371-400 Abstract: We consider a system of real-valued spins interacting with each other through a mean-field Hamiltonian that depends on the empirical magnetisation of the spins. The system is subjected to a stochastic dynamics where the spins perform independent Brownian motions. Using large deviation theory we show that there exists an explicitly computable crossover time tc∈[0,∞] from Gibbs to non-Gibbs. We give examples of immediate loss of Gibbsianness (tc=0), short-time conservation and large-time loss of Gibbsianness (tc∈(0,∞)), and preservation of Gibbsianness (tc=∞). Depending on the potential, the system can be Gibbs or non-Gibbs at the crossover time t=tc. Keywords: Mean-field model; Potential; Independent Brownian motions; Gibbs versus non-Gibbs; Dynamical transition; Large deviation principle; Global minimisers of rate functions (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:1:p:371-400 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2014.09.011 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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