  We investigate whether Gamma-Ray Bursts (GRBs) from the Current BATSE Catalog
have been affected by weak lensing by the nearby large scale structure. The
redshift distribution of GRBs is believed to be broad, extending to z~5, so
most events can be assumed to be at large redshifts, and hence subject to weak
lensing, which would betray itself as projected (anti-)correlations between GRB
events and galaxies or clusters that trace the intervening mass. Given the
observed distribution of GRBs in fluence, and statistical positional error, e,
we predict that most subsets drawn from BATSE Catalog will be anti-correlated
with the foreground structure due to weak lensing, i.e. will show negative
magnification bias. We find that GRBs are indeed anti-correlated with the APM
galaxies (z~0.2-0.3) in the sense that galaxy density in circles of radii 1-1.5
deg (15-20 Mpc at z~0.3) centered on e<1 GRBs is about 10% lower than expected
from a random distribution; the significance of GRB-APM anti-correlations
reaches 99.7%. Cross-correlation between GRBs and distant rich
Abell-Corwin-Olowin clusters is also negative. Standard cosmological models
with Omega_matter ~ 0.3, Omega_Lambda ~ 0.7, and matter distribution on large
scales following observed APM galaxy distribution with the biasing parameter of
around 1 are not able to reproduce our GRB-APM anti-correlations. We propose a
speculative model that does account for these anti-correlations as well as
positive correlations found previously, between QSOs and APM galaxies. We
briefly discuss if the proposed scheme is in conflict with observations of
cosmic microwave background, galaxy surveys, cosmic velocity flows, and weak
shear lensing.
