The Impact of Strong Gravitational Lensing on Observed Lyman-Break
  Galaxy Numbers at 4<z<8 in the GOODS and the XDF Blank Fields
  Detection of Lyman-Break Galaxies (LBGs) at high-redshift can be affected by
gravitational lensing induced by foreground deflectors not only in galaxy
clusters, but also in blank fields. We quantify the impact of strong
magnification in the samples of $B$, $V$, $i$, $z$ $\&$ $Y$ LBGs ($4\lesssim z
\lesssim8$) observed in the XDF and GOODS/CANDELS fields, by investigating the
proximity of dropouts to foreground objects. We find that $\sim6\%$ of bright
LBGs ($m_{H_{160}}<26$) at $z\sim7$ have been strongly lensed ($\mu>2$) by
foreground objects. This fraction decreases from $\sim 3.5\%$ at $z\sim6$ to
$\sim1.5\%$ at $z\sim4$. Since the observed fraction of strongly lensed
galaxies is a function of the shape of the luminosity function (LF), it can be
used to derive Schechter parameters, $\alpha$ and $M_{\star}$, independently
from galaxy number counts. Our magnification bias analysis yields
Schechter-function parameters in close agreement with those determined from
galaxy counts albeit with larger uncertainties. Extrapolation of our analysis
to $z\gtrsim 8$ suggests that future surveys with JSWT, WFIRST and EUCLID
should find excess LBGs at the bright-end, even if there is an intrinsic
exponential cutoff of number counts. Finally, we highlight how the
magnification bias measurement near the detection limit can be used as probe of
the population of galaxies too faint to be detected. Preliminary results using
this novel idea suggest that the magnification bias at $M_{UV}\sim -18$ is not
as strong as expected if $\alpha\lesssim -1.7$ extends well below the current
detection limits in the XDF. At face value this implies a flattening of the LF
at $M_{UV}\gtrsim-16.5$. However, selection effects and completeness estimates
are difficult to quantify precisely. Thus, we do not rule out a steep LF
extending to $M_{UV}\gtrsim -15$.
