AGN While—starting from the very early works (e.g., Seldner and Peebles 1978; Longair and Seldner 1979; Hill and Lilly 1991; Peacock and Nicholson 1991; Allington-Smith et al. 1993; Zirbel 1997)—virtually all the studies presented in the literature converge at indicating that radio-AGN preferentially reside within overdense structures, the three (or rather five if one also includes cross-correlation studies) methods presented in Sect. 4 provide different information on the large-scale structure behaviour of these objects. To summarize them in a few words, we might say that the method based on clustering returns more information on the very large/cosmological (i.e., at Mpc level and beyond) scales traced by radio sources and also on the dark matter content of the regions that host them. On the other hand, very different results are obtained if one searches for structures around known radio-AGN or if one pinpoints radio-AGN within known structures. Indeed, in the first case one finds that virtually all radio-AGN are surrounded by over-densities (e.g., Venemans et al. 2007; Mayo et al. 2012; Galametz et al. 2012; Castignani et al. 2014; Wylezalek et al. 2013; Rigby et al. 2014), while the second method shows that only about 20–30% of them inhabit rich (group- and cluster-like) structures (e.g., Best et al. 2007; Magliocchetti and Brüggen 2007; Lin and Mohr 2007; Croft et al. 2007; Magliocchetti et al. 2018b; Croston et al. 2019). The reason for this discrepancy is not known, but it is likely related to the different redshift ranges probed by the two methods (much more local sources are considered in the second one), and/or—under the assumption of a strong correlation between radio luminosity and environmental density (e.g., Bardelli et al. 2010; Magliocchetti et al. 2018b; Croston et al. 2019; Mo et al. 2020, but see further in this section for different points of view)—to the fact that generally the first method images much brighter radio sources than the second one. In any case, we note that these findings also have implications for the life-time of the radio-AGN phenomenon, and it is therefore of no surprise if works based on the different methods illustrated above find different values, ranging from ∼60\documentclass[12pt]{minimal}
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				\begin{document}$$\sim 60$$\end{document} Myr up to a few Gyr (e.g., Lin and Mohr 2007; Smolčić et al. 2011; Hatch et al. 2014; Magliocchetti et al. 2017). We also note that recent studies based on direct LOFAR observations which—we remind—sample lower frequencies and therefore older emission, would tend to better agree with the high-end values provided above for the radio-active phase of an AGN (τ>200\documentclass[12pt]{minimal}
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				\begin{document}$$\tau > 200$$\end{document} Myr – Heesen et al. 2018).
Citation: Magliocchetti et al. 2018b
Citation function: Differences; Differences