literature, see, for example [@Khan-Moura; @das2015distributed]. Reference [@Khan-Moura] considers the estimation of a time-varying random field pertaining to a linear observation model, where each agent reconstructs only a few components of the field. However, in contrast with [@Khan-Moura] where the incorporation of new sensed information is followed by multiple rounds of consensus, the proposed algorithm in this paper simultaneously fuses the neighborhood information and the current observation albeit for a static field. In contrast with [@das2015distributed], where each agent tries to reconstruct the entire time-varying random field, the proposed algorithm reconstructs only a subset of the components of the entire field at each agent and the information exchange entails a low dimensional vector instead of the entire parameter. Distributed estimation schemes involving objectives where agents reconstruct only a few entries of the parameter have also been studied in [@kekatos2013distributed; @bogdanovic2014distributed; @nassif2017diffusion]. In particular, as compared to [@kekatos2013distributed; @bogdanovic2014distributed; @nassif2017diffusion] which consider static connected communication graphs, in this paper we consider time-varying stochastic communication graphs that are connected on average. In [@nassif2017diffusion] so as to facilitate adaptation, the algorithm employs constant step sizes and the residual mean square error is characterized in terms of the step size only. However in comparison, 