Holographic Brownian motion in 2+1 dimensional hairy black holes

In this paper, we investigate the dynamics of a heavy quark for plasmas corresponding to three dimensional hairy black holes. We utilize the AdS/CFT correspondence to study the holographic Brownian motion of this particle with different kinds of hairy black holes. For an uncharged black hole in the low frequency limit we derive analytic expressions for the correlation functions and the response functions and verify that the fluctuation–dissipation theorem holds in the presence of a scalar field against a metric background. In the case of a charged black hole, we think that the results are similar to that derived for an uncharged black hole.