tokens: available to be detected by standard methods. These proto-clusters, likely lying at , are assumed to be in an active star-forming phase, but not yet fully virialized. To investigate these earlier evolutionary stages we need different approaches, such as the one presented in this paper. During the past decade, more and more proto-cluster candidates have been detected through different techniques, using X-ray signatures, stellar mass overdensities, Ly emission, and association with radio galaxies (e.g., Brodwin et al. 2005 ; Miley et al. 2006 ; Nesvadba et al. 2006 ; Doherty et al. 2010 ; Papovich et al. 2010 ; Hatch et al. 2011 ; Gobat et al. 2011 ; Stanford et al. 2012 ; Santos et al. 2011 , 2013 , 2014 ; Brodwin et al. 2010 , 2011 , 2013 ). However, only a few detections have been done in random fields (e.g., Steidel et al. 1998 , 2005 ; Toshikawa et al. 2012 ; Rettura et al. 2014 ), and most of these detections are biased towards radio galaxies or quasars ( Pentericci et al. 2000 ; Kurk et al. 2000 , 2004 ; Venemans et al. 2002 , 2004 , 2007 ; Galametz et al. 2010 , 2013 ; Rigby et al. 2013 ; Wylezalek et al. 2013 ; Trainor Steidel 2012 ; Cooke et al. 2014 ; Noirot et al. 2016 ), or obtained over very limited fractions of the sky, e.g., in the COSMOS field, which is 1.65 ( Capak et al. 2011 ; Cucciati et al. 2014 ; Chiang et al. 2014 ) and in the Hubble Space Telescope Ultra-Deep Field ( Beckwith et al. 2006 ; Mei et al. 2015 ) with its area. Since the expected surface density of such massive proto-clusters is fairly small, a few times ( Negrello et al. 2007 , 2010 ), performing an unbiased analysis of this population of sources requires us to explore much larger regions of the sky. This has been initiated, for example with the Spitzer SPT Deep Field survey covering 94 and has yielded the detection of 300 galaxy cluster candidates with redshifts ( Rettura et al. 2014 ). The submm and mm sky has proved to be an efficient window onto star-forming galaxies with redshifts between 1 and 6, since it allows us to detect the redshifted modified blackbody emission coming from the warm dust in galaxies. Taking advantage of the so-called negative k-correction in the submm ( Franceschini et al. 1991 ), which compensates for the cosmological dimming at high redshift in the submm, many samples of high- galaxies and also proto-cluster candidates have been identified or discovered in this frequency range in the last two decades (e.g., Lagache et al. 2005 ; Beelen et al. 2008 ; Smail et al. 2014 ). As predicted by Negrello et al. (2005) , Clements et al. (2014) showed that the proto-cluster population can be efficiently detected in the submm as overdensities of dusty star-forming galaxies, which has been made possible thanks to the the observations of larger fields in the submm and mm range. The first discoveries of strongly gravitationally lensed galaxies at very high redshift (e.g., Walsh et al. 1979 ; Soucail et al. 1987 ) opened another window onto the
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