Le Boudec, Jean-Yves The stationary behaviour of fluid limits of reversible processes is concentrated on stationary points. (English) Zbl 1278.60143 Netw. Heterog. Media 8, No. 2, 529-540 (2013). Suppose that \((Y^N)\) is a sequence of càdlàg stochastic processes on \([0,\infty)\) with values in a Polish space \(E\). Assuming existence of a deterministic continuous one-sided time flow \(\varphi\) on \(E\) such that \(Y^N\) converges to \(\varphi\) (the “fluid limit”) in a suitable sense, the following is proved: If \(Y^N\) is reversible with respect to some (then necessarily invariant) probability measure \(\pi^N\) on \(E\) for every \(N\), and if \(\pi\) is an accumulation point (in the topology of weak convergence) of the sequence \((\pi^N)\), then \(\varphi\) is reversible with respect to \(\pi\). Furthermore, \(\pi\) is concentrated on the set of fixed points of the fluid limit \(\varphi\). Reviewer: Hans Crauel (Frankfurt am Main) Cited in 3 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 37A60 Dynamical aspects of statistical mechanics 82C22 Interacting particle systems in time-dependent statistical mechanics Keywords:fluid limit; reversible; fixed points; stationary points; mean field limit; hydrodynamic limit PDFBibTeX XMLCite \textit{J.-Y. Le Boudec}, Netw. Heterog. Media 8, No. 2, 529--540 (2013; Zbl 1278.60143) Full Text: DOI arXiv