Since gravitational lensing effects directly probe inhomogeneities of dark
matter, lensing-galaxy cross-correlations can provide us important information
on the relation between dark matter and galaxy distributions, i.e., the bias.
In this paper, we propose a method to measure the stochasticity/nonlinearity of
the galaxy bias through correlation studies of the cosmic shear and galaxy
number fluctuations. Specifically, we employ the aperture mass statistics
$M_{ap}$ to describe the cosmic shear. We divide the foreground galaxy redshift
$z_f<z_s$ into several bins, where $z_s$ is the redshift of the source
galaxies, and calculate the quantity $^2/$ for
each redshift bin. Then the ratio of the summation of $^2/<
N_g^2(z_f)>$ over the bins to $$ gives a measure of the
nonlinear/stochastic bias. Here $N_g(z_f)$ is the projected surface number
density fluctuation of foreground galaxies at redshift $z_f$, and $M_{ap}$ is
the aperture mass from the cosmic-shear analysis. We estimate that for a
moderately deep weak-lensing survey with $z_s=1$, source galaxy surface number
density $n_b=30 \hbox {gal}/\hbox {arcmin}^2$ and a survey area of $25 \hbox
{deg}^2$, the effective $r$-parameter that represents the deviation from the
linear and deterministic bias is detectable in the angular range of 1'-10' if
|r-1|\gsim 10%. For shallow, wide surveys such as the Sloan Digital Sky
Survey with $z_s=0.5$, $n_b=5 \hbox {gal}/\hbox {arcmin}^2$, and a survey area
of $10^4 \hbox {deg}^2$, a 10% detection of $r$ is possible over the angular
range $1'-100'$.Comment: ApJ in pres